Controlling Translocation Through Nanopores With Fluid Walls

ABSTRACT

Improved resolution and detection of nanoparticles are achieved when a nanopore connecting liquid compartments in a device running on the Coulter principle is provided with fluid coatings such as lipid walls. Fluid lipid walls are made of a lipid bilayer, and preferably include lipid anchored mobile ligands as part of the lipid bilayer. By varying the nature and concentration of the mobile ligand in the lipid bilayer, multifunctional coatings of lipids are provided.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.15/157,591 filed on May 18, 2016, which is a continuation of U.S.application Ser. No. 13/400,472 filed on Feb. 20, 2012, now U.S. Pat.No. 9,347,929 issued May 24, 2016, which claims the benefit of U.S.Provisional Application No. 61/448,093 filed on Mar. 1, 2011. The entiredisclosures of the above applications are incorporated herein byreference.

GOVERNMENT SUPPORT

This invention was made with government support under GM081705 awardedby the National Institutes of Health and DBET0449088 awarded by theNational Science Foundation. The government has certain rights in theinvention.

BACKGROUND

Synthetic nanopores enable fundamental and applied studies of individualbiomolecules in high throughput; their performance is, however, subjectto some limitations.

For example, recordings of resistive current pulses during thetranslocation of molecules through electrolyte-filled nanopores make itpossible to study the size (1-6), conformation (7-8), and activity ofsingle molecules in situ (11-17). This technique can characterizehundreds of unlabeled single molecules per second in physiologicalsolutions and yields distributions of measured parameters from thesesingle-molecule investigations (16,18). Nanopore-based experiments arerelatively simple to set up, execute, and analyze, while providingunique information content including sub-molecular detail on thecomposition of individual molecules (18) and on the formation ofmolecular complexes or aggregates (2,19). In addition, nanopores holdtremendous promise for applied fields such as single-molecule bindingassays (2,16,20), portable detection of (bio)warfare agents (4,5,21),and ultra-fast sequencing of DNA or RNA (22,23). In order to acceleratethe realization of this potential, several challenges should beaddressed; these include:

-   -   Difficulty to fabricate synthetic nanopores reliably on the        (sub-) nanometer scale (24).    -   Difficulty to adjust or actuate the pore diameter, in situ        (25,26).    -   Limited control of translocation times of single-molecule        analytes, often leading to incomplete time resolution of        translocation signals and associated inaccurate determination of        the amplitude and duration of resistive pulses (27-29).    -   Limited control of the surface chemistry inside synthetic pores        (16).    -   Non-specific interactions of analytes with the pore walls        (2,6,30).    -   Pore clogging (16).    -   Low frequency of translocation events at low analyte        concentrations (31); and    -   Poor specificity for analytes (16).

In conventional Coulter counting there are two liquid compartments withan electrode in each compartment and a pore connecting the compartments.The electrodes measure current or other electrical parameters, such asvoltage, resistance, and capacitance, between the two compartments. Whena particle from one of the liquid compartments enters the pore, itperturbs the electric field. The so-called Coulter effect is well-knownand provides that the field is perturbed by a passage of a particlethrough the pore, and the effect is detectable and measurable especiallywhen the pore and the particle are of comparable dimension. As the porediameter decreases, smaller objects can be detected using the Coulterprinciple.

For detection, there must be a measureable change in an electricalparameter for each particle that passes through the pore. It has beentheoretically and empirically found that the length of the pore isimportant, with the result that for small particles like a protein thepore must be very short in order to achieve enough perturbation in theelectrical signal for it to be measured. So, for measuring nano-sizedparticles such as a protein, not only is a small diameter pore requiredbut also a very short pore. Coulter counting of nano-sized particles hasbeen limited by the fact that when a protein or other bio-molecule goesthrough or translocates through a short pore, the transit time is soshort that the best available electronics cannot resolve thetranslocation.

A way of overcoming these and other drawbacks of using the Coulterprinciple on nano-sized analytes would be an advance.

REFERENCES FOR THE BACKGROUND SECTION

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SUMMARY

It has now been surprisingly discovered that improved resolution anddetection of nanoparticles is achieved when a nanopore connecting liquidcompartments in a device running on the Coulter principle is providedwith fluid walls. A fluid wall is provided when a substrate is providedwith a fluid coating. A fluid coating in turn is one in which thediffusion coefficient, measured for example by a conventional FRAP(fluorescence recovery after photobleaching) technique is sufficientlyhigh to provide the noted benefits. In one embodiment, a fluid wall isone in which the measured diffusion coefficient measured by FRAP is atleast 10⁻¹⁸ m² sec⁻¹, at least 10⁻¹⁶ m² sec⁻¹, at least 10⁻¹⁴ m² sec⁻¹,or at least 10⁻¹² m² sec⁻¹. Where the fluid lipid walls are made of alipid monolayer or a lipid bilayer, they can include lipid anchoredmobile ligands as part of the lipid bilayer. By varying the nature andconcentration of the mobile ligand in the lipid bilayer, multifunctionalcoatings of lipids are provided that confer unprecedented capabilitiesto nanopore based sensors. For example, bilayer coatings make itpossible to fine tune and actuate pore diameters in sub-nanometerincrements. Incorporating lipid anchored mobile ligands confersspecificity and slows down the translocation of targeted proteinssufficiently to time resolve translocation events of individualproteins.

In other aspects, advantages are provided because the fluid coatingsprevent pore clogging and enable translocation experiments withproteins, peptide oligomers, fibrils, nucleic acids, and otherbiomolecules. Use of biocompatible fluid coatings described hereinnearly eliminates non-specific binding and makes it possible todistinguish proteins by combined analysis of translocation time, volume,charge, shape, ligand affinity, and so on.

In an illustrative embodiment, a device and a method of use is provided.The device provides for measuring the volume of a biomolecule and forcounting the passage of each biomolecule using the Coulter principle asis conventional in Coulter counting. The device includes a first liquidcompartment, a second liquid compartment, and a synthetic nanoporedisposed between the compartments. The nanopore defines a fluid conduitfrom the first liquid compartment and the second liquid compartment andprovides a path for molecules or other nanoparticles in the firstcompartment to flow to the second compartment. The device also includeselectrodes in both liquid compartments and means for controlling theelectrodes to measure electrical resistance, voltage difference, orionic current flow between the first and second electrodes. In anadvance for application in so-called nano-Coulter counting, thesynthetic nanopore providing a fluid path between the first and secondliquid compartments is lined with a fluid wall. In one embodiment, thefluid wall comprises a lipid bilayer. In another, the fluid wallcomprises a lipid monolayer. In an exemplary embodiment, a dimension ofthe synthetic nanopore perpendicular to the fluid flow direction issub-micrometer, for example on the order of 10 to 500 nm. In preferredembodiments, the dimension is 10 to 50 nm, or 20 to 30 nm.

The length of the fluid path between the first and second liquidcompartments, in the fluid flow direction, is about 10 to about 1000 nm,in an exemplary embodiment. For example, the length is about 10 to 300nm.

A fluid lipid wall lining the nanopore of the Coulter counting device ismade of a lipid bilayer, which can include lipid anchored ligands.Exemplary lipids in the bilayer are phospholipids.

A method of using the device involves introducing a solution containingbiomolecules into the first liquid compartment. The nanopore connectsthe first liquid compartment to the second liquid compartment, enablingdissolved molecules to move through the nanopore. As molecules flowthrough the nanopore, the electric field is perturbed, providing a timebased perturbation of the electric field. In one aspect, theseperturbations are analyzed according to known principles to providevarious measured parameters of the biomolecule, including volume,concentration, and so on. In another aspect, advantage is taken of thefluid walls to measure charge on translocating molecules for the firsttime. Disclosure of this aspect is provided in non-limiting fashion inExample 5 below.

Lipid-coated, synthetic nanopores are multifunctional, fluid, andself-assembling. This meets many of the unmet challenges in nanoporesensing and is particularly beneficial in the context of single-moleculestudies of native proteins. For example, the fluidity of the coatingenables capture and concentration of proteins from dilute solutions andpermits translocation of lipid-anchored proteins at frequencies thatreveal information about their affinity to ligands on these lipidanchors. Fluid coatings also eliminate non-specific adsorption ofproteins to the synthetic walls of the pore, since the surface is fluid,involved in molecular motion, and self-repairing. This effect permitstranslocating captured proteins on top of a fluid, biocompatible coatingsuch as a lipid bilayer and establishes a predictable, quantitativerelationship between translocation times and the charge of individualproteins. The viscous character of the fluid coating slows thetranslocation speed of lipid-anchored proteins and makes it possible tointroduce selectivity for specific biomolecules while resolvingtranslocation events completely in time. These viscous coatingstherefore enable accurate quantitative analyses of the molecular volumeand qualitative analyses of the shape of individual proteins. Theanti-fouling character of fluid coatings made it possible to translocateaggregated forms of disease-relevant amyloid-β (Aβ) peptides through thepore without clogging. This capability permits analyses of the diameter,length, and volume from a large number of individual Aβ oligomers andfibrils during their aggregation in situ.

DRAWINGS

The drawings described herein are for illustrative purposes only ofselected embodiments and not all possible implementations, and are notintended to limit the scope of the present disclosure.

FIG. 1A, FIG. 1B, FIG. 1C, and FIG. 1D illustrate synthetic nanoporeswith bilayer-coated fluid walls. FIG. 1A) Cartoon showing across-section through one sensillum in the antenna of the silk mothBombyx mori. Capture, pre-concentration, and translocation of pheromonesthrough the exoskeleton of these sensilla towards dendrites of olfactoryneurons is thought to occur via lipid-coated nanopores and poretubules³²⁻³⁴. FIG. 1B) Cartoon, drawn to scale, showing a synthetic,lipid-coated (yellow) nanopore in a silicon nitride substrate (grey) andthe interstitial water layer (blue). FIG. 1C) Nanopore resistance andcorresponding open pore diameter as a function of the thickness of thebilayer coating³⁸. Red curve is a best fit of the data to equation (1).Numbers underneath the lipid cartoons refer to the number of carbons intheir acyl chains (see Table 1). FIG. 1D) Actuation of nanoporediameters by a change in the thickness of the bilayer coating, Δd, inresponse to a thermal phase transition of DMPC lipids (see SupplementarySection S1). Blue dotted line and grey shaded region represent the meanvalue and range of phase transition temperatures reported for DMPClipids³⁹. Inset: cycling the temperature between 13° and 27° C. actuatedthe pore diameter dynamically as indicated by the larger changes inelectrical resistance through a pore with (green squares) than without(back squares) a bilayer.

FIG. 2A, FIG. 2B, and FIG. 2C capture affinity-dependentpre-concentration, and translocation of specific proteins after bindingto ligands on mobile lipid anchors. FIG. 2A) Cartoon, drawn to scale,illustrating binding of streptavidin (large particles) to specificlipid-anchored biotin-PE (small circles) followed by single moleculetranslocation of the anchored complex through the nanopore. FIG. 2B)Current versus time traces illustrating capture, pre-concentration, andreduced translocation speed of streptavidin. In the absence of biotingroups, only rare translocation events with short translocation times,t_(d), could be detected in electrolytes containing 6 pM streptavidin(top current trace). In contrast, 0.4 mol % of biotinylated lipids inthe lipid coating strongly increased the event frequency and slowed downthe translocation speed sufficiently to enable complete time resolutionof translocation events (bottom current trace). FIG. 2C) Minimum bulkconcentrations of streptavidin, polyclonal anti-biotin Fab fragments,and monoclonal anti-biotin IgG antibodies required to observe at least30-100 translocation events per second.

FIG. 3A, FIG. 3B, and FIG. 3C illustrate controlling the translocationtimes, t_(d), of single lipid-anchored proteins by the viscosity of thebilayer coating and distinguishing proteins by their most probable t_(d)values. FIG. 3A) Distribution of translocation times of streptavidin.Insets: current versus time traces illustrating that t_(d) could beprolonged more with intermediate viscosity POPC bilayers (bottom currenttraces) than with low viscosity DAPPC bilayers (top current traces).FIG. 3B) Translocation of anti-biotin Fab fragments through nanoporeswith bilayers of intermediate viscosity (POPC) or high viscosity (˜49mol % cholesterol and 50 mol % POPC). FIG. 3C) Translocation ofanti-biotin antibodies through a pore with a coating of intermediateviscosity (POPC). Curves represent a best fit of the corresponding datato a biased diffusion first passage time model¹⁴ (equation S10 inSupplementary Section S5). All bilayers contained 0.15-0.4 mol %biotin-PE. See Supplementary Sections S7 and S9 for binning methods,errors of t_(d), and measurement errors.

FIG. 4A, FIG. 4B, and FIG. 4C illustrate distribution of ΔI values andcorresponding molecular volumes and shape factors of individual proteinstranslocating through bilayer-coated nanopores with biotinylated lipids.FIGS. 4A-4C, Translocation of streptavidin (FIG. 4A), anti-biotin Fabfragments (FIG. 4B) and anti-biotin antibodies (FIG. 4C); the dashedvertical lines indicate ΔI values that would be expected for IgGantibodies with a volume of 347 nm³ and different shape factors γ; seeSupplementary Section S6 for a schematic illustration and discussion ofshape factors^(52,55).

FIG. 5 is a comparison of experimental and theoretical values ofcharge-dependent translocation times of streptavidin. Experimentalvalues are shown in black squares and the curve represents thetheoretical prediction by equation 3. Dashed black line corresponds tothe expected translocation time for streptavidin assuming atranslocation event due purely to diffusion in one dimension(t_(d)=l_(p)>² (2D_(L)), i.e. without an electrophoretic effect. Thevalence |z| of the net charge of streptavidin was varied by the pH ofthe electrolyte⁵⁶. The length of the pore with the bilayer coating was28±0.2 nm. Note that the curve is not a best fit to the data; it is theprediction of t_(d) as a function of |z| according to equation (3) whenall parameters were fixed to their known values.

FIG. 6A and FIG. 6B illustrate bilayer-coated nanopores that resistclogging and enable the monitoring of the aggregation of amyloid-beta(Aβ) peptides. FIG. 6A, Cartoon illustrating clogging of uncoatednanopores and a typical current versus time trace during clogging of ananopore by Aβ aggregates. This concatenated current trace shows several1 s recordings and one 5 min recording. FIG. 6B, Cartoon illustratingtranslocation of individual Aβ aggregates through a bilayer-coatednanopore with a fluid wall (white arrow in the inset) and a typicalcurrent versus time trace of translocation events. The bilayer coatingconferred non-fouling properties to these pores and enabled resistivepulse recordings over at least 40 min without clogging. Both recordingsare 5 s long, one was taken immediately after addition of the Aβ sampleand the other one 40 min later. Aβ (1-40) samples were aggregated for 72h.

FIG. 7 is a diagram of a device operating under the Coulter principle.References in the captions of FIGS. 8-12 are those listed in Example 7.

FIG. 8A and FIG. 8B—Nanopores with fluid walls make it possible tocharacterize Aβ aggregates by resistive pulse recordings. FIG. 8A.Illustration of the experimental setup with fluid access channels to ananopore embedded in a silicon nitride chip.^(54,55)Silver-silver/chloride electrodes immersed in the two fluidiccompartments are connected to a patch-clamp amplifier and used tomeasure the ionic current through the nanopore. Inset left. Cartoonshowing a cross-section of a nanopore that is coated with a fluid lipidbilayer, thereby enabling the translocation of Aβ aggregates withoutclogging of the pore. Inset right. Original current trace showing acharacteristic resistive pulse with the parameters ΔI and t_(d). FIG.8B. Original current traces recorded before adding Aβ, after adding Aβthat was permitted to aggregate for 1 or 3 days. The nanopore had alength of 18 nm and a diameter of 28 nm before the lipid bilayer coating(length of 28 nm and a diameter of 18 nm after the bilayer coating).

FIG. 9A and FIG. 9B—scatter plots of ΔI values versus t_(d) values fromthe translocation of individual Aβ aggregates reveal clusters oftranslocation events due to spherical oligomers, protofibrils withlengths shorter than the length of the nanopore, protofibrils withlengths longer than the length of the nanopore, and mature fibers. FIG.9A) Scatter plots of ΔI(t_(d)) from aggregates of Aβ₍₁₋₄₀₎ that wereanalyzed after 0, 1, 2, and 3 days of incubation. FIG. 9B) Scatter plotof all data combined and color coded according to the results fromstatistical cluster analysis.⁵⁶

FIG. 10A, FIG. 10B, FIG. 10C, and FIG. 10D show a transmission electronmicroscopy (TEM) analysis of the size of Aβ₍₁₋₄₀₎ aggregates. FIG. 10A.Micrographs showing aggregates with increasing size after incubation inwater for 0, 1, 2 and 3 days. FIG. 10B & FIG. 10C. Histograms of thediameters (FIG. 10B) and lengths (FIG. 10C) of all aggregates that werenot mature fibers. Inset in FIG. 10C. Proportion of aggregates withlengths longer than 10 nm and 45 nm. FIG. 10D. Boxplots characterizingmature fibers after three days of aggregation. The fibers werecharacterized by their apparent widths when lying flat w₂ (red arrows inFIG. 10A) on the TEM grid and when twisted or crossing over themselvesw₁ (blue arrows in FIG. 10A) on the TEM grid.²² The box represents therange between the 1^(st) and 3^(rd) quartiles, the dashed linerepresents the median, the dot is the mean, and the whiskers extend tothe range of the data (minimum and maximum values) except for outliers,which are plotted as “x”.

FIG. 11 is estimated lengths of Aβ₍₁₋₄₀₎ protofibrils in clusters (i)and (ii). The lengths of protofibrils were estimated by solving a systemof equations for ΔI (γ, l_(M)) and γ (l_(M)) and assuming that allaggregates were cylindrical. The dotted lines indicate the location oflocal maxima in the size distributions of Aβ₍₁₋₄₀₎ predicted by Cabrioluet al. The local maxima of the Gaussian fits to the data are located at:5.3, 7.0, 10.3, 13.5, and 19.9 nm. Note that the two histograms havedifferent bin-widths and are not normalized.

FIG. 12 consists of frequency of translocation events organized bycluster classification reveal time-dependent aggregation. Mean valuesand standard deviations were calculated by counting the number oftranslocation events within a given cluster classification duringseveral recordings totaling 40-100 s in duration.

FIG. 13A and FIG. 13B Schematic cross-section of the silicon chip and ofthe nanopore with the channel leading to the pore. FIG. 13A) Siliconchip (dark) with a silicon nitride layer (gray) on the top; thefree-standing part of this Si3N4 layer constitutes a window with ananopore and with a channel through the silicon nitride that leads tothe pore. FIG. 13B) Schematic illustration of this channel with a lengthl_(C) of 258±9 nm and a radius r_(C) of 50±7.5 nm, which led to ananopore with radii r_(P) of 16-50 nm and lengths 1p of 12-22 nm,depending on the chip. Schematic illustration of a lipid bilayer coatingwith a thickness d and a water layer between the bilayer and the chipwith a thickness wL; this bilayer coating increases the effective lengthof the nanopore to lP′=lP+2(wL+d) and reduces the effective radius torP′=rP−wL−d.

FIG. 14A, FIG. 14B, FIG. 14C and FIG. 14D illustrate transmissionelectron micrographs of several nanopores used in this work. Thebrightest part in the center of each image depicts the shape and size ofthe nanopore and the surrounding circle with reduced brightness reflectsthe channel leading to the nanopore. All scale bars are 50 nm. FIG. 14A)Pore used for experiments with bilayers that contained lipids withdifferent acyl-chain lengths (<rP>=14 nm, lP=12 nm, rC=48 nm, and lC=264nm).

FIG. 14B) Pore used for sensing streptavidin (<rP>=9.6 nm, lP=18 nm,<rC>=49 nm, and lC=258 nm). FIG. 14C) Pore used for sensing monoclonalanti-biotin antibody and anti-biotin antibody Fab fragment (<rP>=16.5nm, lP=22 nm, <rC>=53 nm, and lC=255 nm). FIG. 14D) Pore used forsensing aggregates of Aβ peptides. For these experiments, the channelcreated by a focused ion beam without sculpting was used as the pore(<rP>=48 nm and lP=275 nm; rC=0 and lC=0). Notation of a radius as <r>indicates an area-equivalent radius calculated with equations (S4) or(S5). All dimensions refer to the pores before bilayer coating.

FIG. 15 is shrinking and actuating the diameter of bilayer-coatednanopores with temperature. Resistance as a function of temperature in ananopore coated with a bilayer of DMPC lipids, (circles), and in a porewithout a bilayer coating, (squares). The bottom curve (-) represents aphysical model based on equations (S3), (S7), and (S8) and described theresistance through the uncoated nanopore. Inclusion of the bilayerthickness, d, as a fitting parameter by employing equations (S6)-(S8)described the resistance through a bilayer coated-nanopore in thetemperature range from 280 K to 290 K (top curve, R2=0.95, N=5) and inthe temperature range from 300 K to 310 K (middle curve, R2=0.97, N=5).The dimensions of the nanopore before bilayer formation were rP=13 nm,lP=28 nm, rC=50 nm, and lC=247 nm. The recording buffer contained 500 mMKCl and 10 mM HEPES (pH 7.4±0.1), and the applied potential differencewas ±0.1 V.

FIG. 16A, FIG. 16B, FIG. 16C, and FIG. 16E describe fluorescencemicrographs of Si—Si3N4 chips with a supported lipid bilayer containingRh-PE lipids and corresponding line scans. FIG. 16A) Epifluorescencemicrograph with a line scan to quantify the fluorescence intensity alongthe path shown by the solid white line. This pore had an area-equivalentdiameter of 33.5 nm and a length of 22 nm without the bilayer coating.FIG. 16B) Plot of fluorescence intensity as a function of position alongthe line scan. The numbers 1-4 correspond to the numbers in FIG. 16A tothe location on the chip indicated in the schematic illustration FIG.16C. FIG. 16E) Additional epifluorescence micrographs showing thediffraction limited spot at the location of the nanopore. Line scanswere measured from the opposite corners of the silicon nitride windowsimilar to that in panel FIG. 16A. From top to bottom these pores hadarea-equivalent diameters of 31 nm, 33.5 nm, and 20 nm; and lengths of20 nm, 22 nm, and 18 nm. All bilayers were labeled with 0.8 mol % Rh-PE.All scale bars correspond to 10 μm.

FIG. 17A and FIG. 17B describe fluorescence micrographs for determiningbilayer fluidity by fluorescence recovery after photobleaching (FRAP)experiments. FIG. 17A, Epifluorescence micrographs indicating therecovery of fluorescence in a photobleached spot of the lipid bilayer onthe Si—Si3N4 chip. FIG. 17B, Plot of intensity versus time from twoseparate FRAP experiments on a chip that was coated with a bilayercontaining 98.8 mol % POPC (▪) or with 98.8 mol % DΔPPC (●). The largert½ value for POPC lipids compared to DΔPPC lipids indicated theincreased viscosity of POPC bilayers compared to DΔPPC bilayers. Allbilayers were labeled with 0.8 mol % Rh-PE and contained 0.4 mol % of1,2-dipalmitoyl-sn-glycero-3-phosphoethanolamine-N-(cap biotinyl)(biotin-PE) because the same chips were later used to sense thetranslocation of streptavidin (FIG. 3A and FIG. 4A). Images in a wereboth contrast enhanced to the same extent to increase clarity. The scalebars correspond to 25 μm.

FIG. 18A and FIG. 18B describe fluorescence micrographs ofsilicon-nitride windows with a nanopore after exposure to fluorescentlylabeled-streptavidin. FIG. 18A, Fluorescence micrograph taken of thesilicon nitride window after physisorption of streptavidin-TRITC onto achip that was cleaned with a fresh 3:1 mixture of concentrated sulfuricacid and a 30% (v/v) hydrogen peroxide solution (Piranha solution). Theline scan beneath the image corresponds to the intensity of fluorescencealong a diagonal path across the silicon nitride window through thelocation of the nanopore at its center. FIG. 18B, Fluorescencemicrograph taken of the same silicon nitride window but after formationof a supported lipid bilayer of POPC lipids followed by incubation withstreptavidin-TRITC. The line scan beneath the image corresponds to theintensity of fluorescence along a diagonal path across the siliconnitride window through the location of the nanopore at its center. Thenanopore for these experiments had an area-equivalent diameter of 110 nmand a length of 275 nm. Scale bars correspond to 10 μm. The same cameraand exposure settings were used to acquire both images.

FIG. 19A, FIG. 19B, FIG. 19C and FIG. 19D contain power spectra of theelectrical current noise from chips with a bilayer coating and fromchips without a bilayer coating. FIG. 19A, FIG. 19B, Power spectra ofthe noise before and after formation of supported lipid bilayers fromtwo different lipids on the same chip while a voltage of −0.1 V wasapplied. The nanopore had a diameter of 28 nm before formation of thesupported lipid bilayer (FIG. 19A, POPC lipids; FIG. 19B, DΔPPC lipids).In FIG. 19B, the current recording was recorded with the hardware filterof the amplifier set to a cut-off frequency of 2 kHz. FIG. 19C, FIG.19D, Power spectra of the noise from two independent experiments with achip containing a very small area-equivalent diameter of 9 nm, which wastoo small for the formation of a lipid bilayer inside the nanopore. InFIG. 19D, the current recording was recorded with the hardware filter ofthe amplifier set to a cut-off frequency of 2 kHz. The electrolyte forall recordings contained 500 mM KCl and 10 mM HEPES with a pH of7.4±0.1.

FIG. 20—Nanopore coatings with increasing mole fractions of negativelycharged lipids reduce the resistance of the nanopore in electrolyteswith low ionic strength. The supported lipid bilayers were formed fromliposomes with the indicated mole fractions, X_(PA), of DOPA lipids witha background of POPC lipids. The pore used for these experiments had adiameter of 28 nm before the bilayer coating. The electrolyte had anionic strength of ˜2.5 mM and contained 750 μM CaCl₂ and 250 μM KCl witha pH of ˜7.

FIG. 21 describes charges on the surface of a pore with a diameter of0.5 μm did not significantly affect the permeation of ions, and henceresistance, through the pore. Currents were measured as a function ofapplied potential difference through a conical pore (tip diameter 500nm) without a bilayer (▪), through the same pore with an electricallyneutral bilayer coating of POPC lipids (

), and through the same pore with a bilayer coating containing 40 mol %of negatively charged lipids (

). The recording electrolyte was the same as in Fig. S8.

FIG. 22A, FIG. 22B, and FIG. 22C are bar graphs comparing the frequencyof resistive pulses due to the translocation of streptavidin,anti-biotin mAb, and anti-biotin Fab fragments through bilayer-coatednanopores with biotin-PE lipids and respective control experiments. FIG.22A, Frequency of resistive pulses due to translocation of SA through ananopore with a bilayer coating that contained biotin-PE lipids andafter exchanging the electrolyte for 3 h to remove SA from solutioncompared to a coating without biotin-PE lipids (in this case thefrequency of events was 0.09 s⁻¹ and is too low to be seen as a bar).FIG. 22B, Frequency of resistive pulses due to the translocation ofanti-biotin mAb through a nanopore with a bilayer coating that containedbiotin-PE lipids compared to the same experiment after adding 10 μM ofsoluble biotin to the solution and compared to an experiment with ananopore coating that did not contain biotin-PE lipids. FIG. 22C,Frequency of resistive pulses due to the translocation of anti-biotinFab through a nanopore with a bilayer coating that contained biotin-PElipids compared to a coating without biotin-PE lipids. Theconcentrations of the proteins are shown above the bars. Bilayers wereformed from ˜99 mol % POPC, 0.8 mol % Rh-PE, and if indicated, 0.15 mol% biotin-PE.

FIG. 23A, FIG. 23B, and FIG. 23C are a description of detection ofmonoclonal anti-biotin IgG₁ antibody (mAb) with a bilayer-coatednanopore. FIG. 23A, Current versus time trace showing resistive pulsesdue to translocation of mAbs that were bound to biotin-PE lipids in thebilayer coating and analysis of t_(d) and ΔI of the correspondingresistive pulses. Resistive pulses occurred at a frequency of 34 s⁻¹.FIG. 23B, Current versus time trace recorded after the addition ofexcess biotin (10 μM) to the solution, illustrating the reducedfrequency of resistive pulses (1.3 s⁻¹) and analysis of t_(d) and M ofthe corresponding resistive pulses. FIG. 23C, Current versus time tracerecorded using the same nanopore as a and b but with a bilayer coatingthat did not contain biotin-PE lipids, illustrating the reducedfrequency (2 s⁻¹) of resistive pulses even at a concentration of mAb of25 nM and analysis of t_(d) and ΔI of the corresponding resistivepulses. Distributions of t_(d) values were fit with equation (S10) asdescribed in Supplementary Section S5.4 and S7.1. Bilayers were formedfrom ˜99 mol % POPC, 0.8 mol % Rh-PE, and if indicated, 0.15 mol %biotin-PE. The experiments were performed with the nanopore shown inFIG. 14C. The recording buffer contained 2.0 M KCl and 10 mM HEPESbuffered at a pH of 7.4±0.1, and currents were recorded at an appliedpotential difference of −0.1 V.

FIG. 24A, FIG. 24B, FIG. 24C, and FIG. 24D describe viscosity ofbilayers which can slow the translocation of anti-biotin Fab fragmentsthat are bound to biotin-PE lipids permitting time-resolveddetermination of the peak amplitude of resistive pulses. FIG. 24A,Current traces showing resistive pulses due to the translocation of Fabfragments through the nanopore. Resistive pulses were observed at afrequency of ˜100 s⁻¹ with bilayer coatings that contained biotin-PE,whereas bilayer coatings without biotin-PE resulted in resistive pulsesat a frequency of 2 s⁻¹. FIG. 24B, Individual resistive pulses fromtranslocation of Fab fragments through a bilayer-coated nanoporecontaining 99.2 mol % POPC and 0.8 mol % Rh-PE in the bilayer coating(but no biotin-PE) and analysis of t_(d) and ΔI of theseresistive-pulses. FIG. 24C, Individual resistive pulses fromtranslocation of Fab fragments through a bilayer-coated nanoporecontaining 0.15 mol % biotin-PE, ˜99 mol % POPC, and 0.8 mol % Rh-PE andanalysis of t_(d) and ΔI of these resistive-pulses. FIG. 24D, Individualresistive-pulses from translocation of Fab fragments through a nanoporecoated with a bilayer of increased viscosity (containing 0.15 mol %biotin-PE, 49.5 mol % POPC, 49.5 mol % cholesterol, and 0.8 mol % Rh-PE)and analysis of t_(d) and ΔI of these resistive-pulses. Distributions oft_(d), except the incomplete distribution in FIG. 24B, were fit withequation (S10) as described in Supplementary Section S5.4 and S7.1. Theexperiments were performed with the nanopore shown in FIG. 24C. Therecording buffer contained 2.0 M KCl and 10 mM HEPES buffered at a pH of7.4±0.1. Currents were recorded at an applied potential difference of−0.1 V.

FIG. 25A and FIG. 25B illustrate two extremes of possible orientationsof an IgG antibody, approximated by an oblate spheroid, during itstranslocation through a nanopore. FIG. 25A, Cartoon illustrating thetranslocation of an oblate spheroid with its pole-to-pole axis orientedperpendicular to the length axis of the pore; this orientation wouldresult in a shape factor, γ, of 1.1. FIG. 25B, Illustration of the sameoblate spheroid as in FIG. 25A but translocating through the pore withits equatorial axis oriented perpendicular to the length axis of thepore; this orientation would result in a shape factor, γ, of 5.0. Notethat the illustration is drawn to scale and that the nanopore was drawnto match the dimensions of the pore used for the experiments in FIG. 4Cof the main text. A scaled space-filling model of an IgG antibody³⁰ witha volume of 347 nm³ overlays the oblate spheroid with the same volume.

FIG. 26A and FIG. 26B—Translocation of non-spherical lipid-anchoredstreptavidin-IgG complexes resulted in broad distributions of ΔI due tothe various orientations the complex could assume inside the nanopore.FIG. 26A, Distributions of ΔI and t_(d) resulting from the translocationof streptavidin while bound to biotin-PE lipids in the bilayer coatingof a nanopore. FIG. 26B, Distributions of ΔI and t_(d) after theaddition of a biotinylated polyclonal, IgG antibody against catalase.Note that before recording resistive pulses, the electrolyte solutionswere thoroughly rinsed to remove unbound proteins from the solution. Thebilayer coating in this experiment contained 0.15% biotin-PE, 0.8%Rh-PE, and ˜99% POPC. The nanopore had a diameter of 36 nm and a lengthof 26 nm with the bilayer coating.

FIG. 27 is cumulative distributions of t_(d) obtained from translocationevents of mAb at different applied voltages. Distributions of t_(d)values were determined from recording translocation events of mAb whileapplying potential differences of 120 mV (upper curve -), 100 mV (secondcurve from top -), 80 mV (middle curve -), 70 mV (second curve frombottom -), and 60 mV (lower curve -) across the chip. The inset showsthe distributions over the range of t_(d) values of 20 μs to 150 μs.Best curve fits of this data to equation (S13) determined the mostprobable values of t_(d) (t_(d, mp)) in order of decreasing appliedpotential difference: 40 μs, 43 μs, 60 μs, 67 μs, and 90 μs.

FIG. 28A, FIG. 28B, and FIG. 28C describe effect of different bin-widthsfor determining the most frequently observed value of t_(d) based onbest curve fits of t_(d) data in histograms to equation (S14). Differentbin-widths of FIG. 28A) 15 μs, FIG. 28B) 30 μs, and FIG. 28C) 50 μs wereused to produce these histograms from t_(d) values that were measuredfrom translocation events of streptavidin in an electrolyte with pH=6.6.These t_(d) histograms were fit with equation (S14) using the non-linearcurve fitting function of the software OriginPro 8 with its so called“Extreme Function”.

FIG. 29 describes most probable t_(d) values for the monoclonalanti-biotin IgG₁ antibody (mAb) as a function of the voltage drop,V_(P), across a bilayer-coated nanopore containing biotin-PE. The redcurve was obtained by a best fit of equation (S18) to the data with z asthe only fitting parameter. The fit returned a value for z of −4.2±0.5with R²=0.94 (N=8). The error bars of the most probable t_(d) values inthis plot are likely overestimates that are based on an 1p of ±1 nmsince all of these recordings were performed on the same chip with thesame bilayer and the variations in 1p between current recordings aremore likely to be ±0.2 nm due to fluctuations in the thickness of thewater layer and lipid bilayer. The bilayer coating in this experimentcontained 0.15% biotin-PE, 0.8% Rh-PE, and ˜99% POPC. After the bilayercoating, the nanopore had a diameter of 36 nm and a length of 24 nm.

FIG. 30A, FIG. 30B, and FIG. 30C contain a capillary electropherogramsfor determining the charge of the proteins used in this work. FIG. 30A,FIG. 30B, Electropherograms obtained with a CE instrument equipped withUV detection. Protein samples were prepared in PBS at pH 7.4 andincluded the neutral marker, 4-methoxybenzyl alcohol. The neutral makerappeared at 15-15.5 min and is labeled in the figure. Peaks due to theprotein are shown in red and the time of each peak's maxima is indicatedin the figure. The capillary was a fused silica capillary with a totallength of 64.5 cm and an internal diameter of 50 μm. The length of thecapillary to the detector was 56 cm and the total applied voltage was 15kV. The temperature of the capillary was maintained at 25° C. FIG. 30C)Electropherogram obtained with a CE instrument equipped withfluorescence excitation at 490 nm and detection at 540 nm. The proteinsample was prepared in PBS at pH 7.4 and included the zwitterionicfluorophore, rhodamine B, which served as the neutral fluorescentmarker. The sample contained 1.8 μM of the anti-biotin IgG mAb and 0.5μM of biotin-5-fluorescein, with a net charge of z=−1. The capillary wasa fused silica capillary with a total length of 30 cm and an internaldiameter of 50 μm. The length of the capillary to the detector was 20 cmand the total applied voltage was 7.0 kV. The temperature of thecapillary in FIG. 30C was maintained at 28° C. Note that in all cases,the baseline of the electropherograms were adjusted.

FIG. 31A and FIG. 31B are a characterization of t_(d) and ΔI for pulsesof various simulated translocation times resulting from an input from awaveform generator. FIG. 31A. Measured values for the pulse magnitude,ΔI, of pulses input into the headstage with a waveform generator. Thedotted line denotes the value of t_(d) at which ΔI was attenuated by 3%(˜50 μs). FIG. 31B. Measured values for the pulse duration of pulsesinput into the headstage with a waveform generator show that t_(d) couldbe accurately determined if it exceeded a threshold value of ˜25 μs.Therefore the lower limit of accurate quantification of t_(d) values was25 μs. The line is plotted with a slope equal to 1.

FIG. 32 is histograms of t_(d) values measured from current pulses withdefined duration and added electrical noise from resistive pulseexperiments. Current pulses with precisely defined durations of 30, 50,70, 100, 120, 140, and 160 μs were combined with electrical noise from aresistive-pulse experiment and the duration of these pulses wasdetermined by their half-width. The red lines were obtained by fittingthe histograms with a Gaussian distribution. From these fits, themeasurement error of t_(d), at, was determined to be 2.3, 4.0, 3.4, 3.9,3.2, 3.2, and 3.4 μs (listed in order of increasing pulse duration).

FIG. 33 is gel electrophoresis results showing aggregation ofamyloid-beta (residues 1-40) as a function of incubation time in water.Lane 1 (0 h), containing a solution of freshly prepared Aβ₍₁₋₄₀₎, showsthat initially most of the Aβ peptides in solution were monomers with amolecular weight of ˜4 kDa. Lanes 2 (24 h), 3 (48 h), and 4 (72 h) showthat as Aβ aggregated in solution for increasing times, it formedaggregates of large molecular weight (6-250 kDa). Furthermore, lanes 2and 3 show a population with a very large molecular weight (greater than250 kDa) that remained in the wells of the polyacrylamide gel as itwould be expected for fibrillar aggregates. The inset shows the same gelbut exposed for 180 s and reveals that aggregates of large molecularweight (greater than 250 kDa), which remained in the well of the gel,were already present after 24 h of aggregation (lane 2). The molecularweight markers were See Blue Plus2 Stained Standard Markers fromInvitrogen.

FIG. 34 is nanopores without a fluid lipid coating clogged after addingAβ₍₁₋₄₀₎. Plot of eight concatenated, 20 sec, current versus timetraces. The time gap between current traces is not to scale. The elapsedtime between adding Aβ₍₁₋₄₀₎ (0.025 mg×mL⁻¹ in the top solutioncompartment) and the last current trace is 231 s, and the average timeinterval between recordings was 15 s. Before adding Aβ₍₁₋₄₀₎, thecurrent was −52 nA, and after adding Aβ₍₁₋₄₀₎ the current decreased to˜−25 nA. The gradual decrease of the current was due to adsorption of Aβon the nanopore walls while the stepwise changes in current presumablyindicate the adsorption and desorption of large aggregates. Note thatafter a few seconds, reliable analysis of Aβ aggregates cannot beperformed, and after two minutes, no more resistive-pulses can beobserved. This experiment proceeded under identical conditions to thosereported in the main text with the exception that the nanopore was notcoated with a lipid bilayer. The Aβ₍₁₋₄₀₎ sample had been permitted toaggregate in pure water for ˜3 h prior to the experiment. The appliedelectric potential difference was −0.2 V.

FIG. 35 shows that nanopores with a fluid lipid coating do not clogafter adding Aβ₍₁₋₄₀₎ thereby permitting characterization of aggregates.Plot of four concatenated current traces that are each 20 s in duration.The time gap between current traces is not to scale. The elapsed timebetween adding Aβ₍₁₋₄₀₎ (0.0125 mg×mL⁻¹ in the top solution compartment)and the last current trace is 180 s. This Aβ₍₁₋₄₀₎ sample had beenpermitted to aggregate in pure water for one day prior to theexperiment. Bilayer-coated nanopores remain usable for sensingresistive-pulses of Aβ aggregates for at least 1.5 h.¹

FIG. 36A and FIG. 36B show gel electrophoresis results showing Aβ₍₁₋₄₀₎aggregates after zero, one, two, and three days of aggregation time.

FIG. 37 is a histogram of translocation times of Aβ aggregates that wereclassified into clusters (i) and (ii). The width of the bins in thehistogram is 10 μs, and the first bin starts at 35 μs since that was theminimum translocation time that could be determined accurately.⁴ As aresult, the complete distribution of translocation times could not beobtained.

FIG. 38 describes a predicted trend in the most-probable translocationtime for aggregates with constant charge per molecular weight whileneglecting electrostatic effects and assuming a spherical aggregate.

FIG. 39A and FIG. 39B show a diameter of protofibrils with variouslengths (FIG. 39A) and diameter of individual protofibrils at variouspositions throughout the length of the aggregate as seen in TEMmicrographs (FIG. 39B). FIG. 39A. Mean diameter of protofibrils withvarious total lengths, l_(M), for protofibrils grouped into bins withlengths ranging from 5 nm to greater than 100 nm. Error bars arestandard error of the mean. FIG. 39B. The diameter of seven aggregatesmeasured at five different locations within the length of the aggregate.Note that the diameter remains relatively constant throughout the lengthof the individual aggregate suggesting that the shape of theseprotofibrils resembles that of a cylinder more than that of a prolate.

FIG. 40A and FIG. 40B show length of aggregates in cluster (i) assumingthat aggregates are free to rotate in three dimensions inside thenanopore (FIG. 40A) and the fraction of the cross-sectional area of ananopore that a horizontal cylinder of length l_(M) could occupy (FIG.40B). The lengths of aggregates in cluster (ii) are the same as thoseplotted in FIG. 3 of the main text and are shown for comparison.

FIG. 41 shows the length of aggregates in clusters (i) and (ii) whendefining their shape and volume as prolate spheroids.

FIG. 42A, FIG. 42B, FIG. 42C, and FIG. 42D show an analysis of the sizeof Aβ₍₁₋₄₀₎ aggregates seen in micrographs taken with a transmissionelectron microscope. FIG. 42A. Micrographs showing aggregates withincreasing size after incubation in pure water for 0, 1, 2 and 3 days.FIG. 42B & FIG. 42C. Histograms of the diameters (FIG. 42B) and lengths(FIG. 42C) of all aggregates that were not mature fibers. Inset in FIG.42C. the proportion of aggregates with lengths longer than 10 nm and 45nm, the effective length of the nanopore, as a function of aggregationtime. FIG. 42D. Boxplots characterizing the mature fibers that formedafter three days of aggregation. The fibers were characterized by theirapparent widths when lying flat (blue arrows in FIG. 42A) on the TEMgrid and when twisted or crossing over itself (red arrows in FIG. 42A)on the TEM grid.²³ The box represents the range between the 1^(st) and3^(rd) quartiles, the dashed line represents the median, the dot is themean, and the whiskers extend to the range of the data (minimum andmaximum values).

DETAILED DESCRIPTION

In one embodiment, a nano-Coulter counter is provided and a method ofusing it. A method of detecting, quantifying, or characterizing abiomolecule or collection of biomolecules using the Coulter principleinvolves providing a transit path for biomolecules to pass through ananopore from a first liquid compartment to a second liquid compartment.The first and second liquid compartments contain electrodes disposed tomeasure voltage, electrical current, or electrical resistance betweenthe two liquid compartments. The method further includes measuring thevoltage difference, electrical current, or electrical resistance betweenthe two liquid compartments over time as individual biomolecules passthrough the nanopore. In the method, the nanopore is a passageway orconduit through a substrate, with the passageway is lined with a fluidwall. In one embodiment, the fluid wall comprises a lipid bilayer andcan contain a lipid anchored ligand that binds individual biomolecules.

The method is further characterized by the nanopore having a nominalwidth (perpendicular to the transit path) that is about 1.5 to about 50times the dimension of the biomolecules. The nanopore is furthercharacterized by a length (parallel to the transit path) of about 1 to 5times its nominal width.

The apparatus and method operate on the Coulter principle. Asbiomolecules pass through or are drawn through the nanopore, it changesthe electrical conductance (or other measureable electric parameter)which is detected by the electrodes and their control means. In effect,the biomolecules alter the effective cross-section of the conductivechannel (the nanopore) through which they pass. If desired, a pluralityof nanopores or nanochannels can be provided to separate the two liquidchambers containing an electrolyte solution. When particles orbiomolecules flow from the first to the second liquid compartment, theelectrical resistance of the liquid filled nanopore/nanochannel ischanged. These changes in electrical resistance (or other electricparameter) are recorded as current or voltage pulses, which in turn arecorrelated to size, electrophoretic and diffusive mobility, surfacecharge, and concentration of the biomolecules, in non-limiting fashion.

In another aspect, a method of measuring the translocation time, ligandaffinity, charge, volume, shape, size, or other characteristic of abiomolecule according to the Coulter principle is provided. The methodinvolves detecting and measuring a change in conductivity, resistivity,resistance, conductance, current flow, voltage, or other electricalparameter measured between two liquid compartments separated by andfluidically coupled through a synthetic nanopore, upon translocation ofa biomolecule such as a protein from one liquid compartment through thenanopore to the other liquid compartment. The nanopore comprises apassageway lined with a fluid wall. In one embodiment, the fluid wallcomprises a lipid bilayer. The method further involves deriving thedesired molecule characteristic from the measured electrical parameter.In preferred embodiments, the nanopore connecting the first and secondcompartments is about 10 to 100 nm in diameter (the dimensionperpendicular to the flow path between the compartments) and is about 10to 50 nm long (the dimension parallel to the flow path).

The changes in the electrical parameter that are measured in the methodarise from the Coulter effect that provides that, in variousembodiments, best results are obtained when the diameter or dimension ofthe molecule is approximately 2% to approximately 65% of the nominaldiameter or dimension of the nanopore.

In another embodiment, a device is provided for measuring a parameter ofa biomolecule using the Coulter principle. Such a “nano-Coulter counter”contains a first liquid compartment and a second liquid compartmentdefining a fluid flow direction from the first to the secondcompartment. A synthetic nanopore is disposed between and provides afluid path between the first and second liquid compartments. There is afirst electrode in the first liquid compartment and a second electrodein the second liquid compartment. In addition, means are provided forcontrolling the electrodes to measure resistance, voltage difference,current flow, or other electrical parameter between the first and secondelectrodes. Advantageously, the synthetic nanopore is a passagewaybetween the first and second liquid compartments lined with a fluidwall, and wherein a dimension of the synthetic nanopore perpendicular tothe fluid flow direction is about 10 to 500 nm, for example, about 10 to100 nm, 10 to 50 nm, or 20 to 30 nm, in non-limiting embodiments.

Further non-limiting description of the various aspects and embodimentsof the invention will now be provided. It is to be understood thatlimitations and features discussed with respect to one embodiment arealso applicable and usable with other embodiments, unless the contextrequires otherwise. In particular, the characteristics of the nanoporeseparating the first and second liquid compartments are common to mostof the aspects of the invention described herein. The nanopore ischaracterized by a width and length, and by the chemical composition ofthe lipid bilayer formed on the wall of the substrate that forms thenanopore.

Coulter Counting

In a device operating according the Coulter principle or Coulter effect,particles suspended—or biomolecules dissolved—in an electrolyte solutionare drawn through a small aperture, separating two electrodes betweenwhich an electric current flows. The aperture is referred to in thecurrent teachings as a nanopore. Nanochannel is sometimes used for thesame concept. The voltage applied across the aperture creates a “sensingzone”. As particles pass through the aperture (or “sensing zone”), theydisplace their own volume of electrolyte, momentarily changing theimpedance of the aperture.

This change in impedance produces a pulse that is digitally processed inreal time. The Coulter Principle states that the pulse is directlyproportional to the tri-dimensional volume of the particle that producedit. Analyzing these pulses enables a size distribution to be acquiredand displayed in volume (nm³, μm³ or fL) and diameter (μm or nm). Inaddition, a metering device is used to draw a known volume of theparticle suspension through the aperture (displayed in FIG. 7 as levelsensors 16 and 18 attached between the first liquid compartment and thecontrol means); a count of the number of pulses can then yield theconcentration of particles in the sample.

The basic non-electronic part of a traditional Coulter counter unit, asshown in FIG. 7, consists of a reservoir (the second liquid compartment20) into which a finger-like tube (the first liquid compartment 10) ispartially immersed. Near the lower end of the tube 10 is a very smallhole 30 of known diameter. (Assortments of tubes are available coveringa large range of hole sizes.) In the current teachings, the hole 30 isthe nanopore discussed further herein.

If the “finger” 10 is filled to some point 12 above the level 14 of theoutside reservoir 20, the contents 40 of the finger will slowly flowthrough the hole 30 until the two levels are equalized. This means thatany particles suspended in or dissolved in the first liquid compartment10 (such as the biomolecules described herein) will get flushed throughthe hole 30 also.

If electrodes (drawn as + and—in FIG. 7 are provided in the finger(first liquid compartment 10) and in the reservoir (second liquidcompartment 20), an electrical current will then also pass through thehole (aperture or nanopore 30) along with the fluid. This current (orany similar parameter such as voltage or resistance) can be monitoredfor irregularities, for example by an oscilloscope type of device. Means50 are provided for controlling the electrodes to monitor and displaythe changes in measured electrical parameters. In various embodiments,the measured parameters are provided as outputs for further manipulationby other modules or calculating means to provide other informationderivable theoretically from the measured pulses.

Conventional Coulter counters are well known and commercially available.Method of controlling the electrodes to measure electrical parametersare provided in various of these commercial embodiments. The theoreticaldevelopment of the derivation of molecular parameters from Coultereffect measurements is also well developed. Means for deriving theparameters are provided in commercial embodiments, and severalalgorithms and procedures for their calculation are also given in theExamples section below, and in references recited therein.

Fluid Coatings

Fluid coatings include those exhibiting a diffusion coefficient asmeasured with conventional fluorescence recovery after photobleaching(FRAP) that is sufficiently high to provide the benefits discussedherein, including the ability of the nano-Coulter counter with fluidwalls to time resolve the translocation events. In various embodiments,the diffusion coefficient is at least 10⁻¹⁸ m² sec⁻¹, at least 10⁻¹⁶ m²sec⁻¹, at least 10⁻¹⁴ m² sec⁻¹, or at least 10⁻¹² m² sec⁻¹. Although theinvention is not limited by theory, it is believed that the viscositycharacteristics of the fluid coatings contribute to the advantagesobserved when using them. In a preferred aspect, the fluid coating isprovided on the nanopore aperture by applying a bilayer or monolayer tothe surface of the substrate in the nanopore aperture. Basically, anymolecule that is amphipathic is potentially capable of forming asuitable bilayer or monolayer on the substrates to provide nanoporeswith fluid walls. Examples include a surfactant or detergent having ahydrophilic group and a hydrophobic group. Other examples includewithout limitation molecules generated from click chemistry thatresemble lipids, such as those described in “Vesicle and stablemonolayer formation from simple “click” chemistry adducts in water” bySantanu Bhattacharya and Joydeep Biswas in Langmuir 2011 ASAP, the fulldisclosure of which is incorporated by reference herein. It is preferredin some embodiments to use surfactant, detergent, or lipid materialsthat have a charged hydrophilic head; in particular embodiments,phospholipids are preferred.

When the surface to which the coating is applied is hydrophilic,amphipathic molecules form or self-assemble on the substrate to makebilayers. When the surface is hydrophobic (or is modified to behydrophobic, such as by silanization or other technique), amphipathicmolecules tend to form a monolayer. In the monolayer, the hydrophobictail of the amphipathic molecule is attracted to the hydrophobic surfaceso that the hydrophilic head of the molecule is exposed to the solutionbeing tested. When the substrate has a hydrophilic surface, it attractsthe hydrophilic head of the amphipathic molecule, and a bilayer formssuch that the hydrophilic head of the second layer is exposed to thesolution.

Lipid Coatings

When lipids are applied, they form fluid lipid walls on the nanopore.The lipids that make up the lipid bilayers or monolayers formed on thewalls of the substrate to provide the nanopores are amphipathic, havinga hydrophilic head and a hydrophobic tail.

Lipid bilayers and monolayers can be applied to the surface of thesubstrate to provide the nanopores with fluid walls, for example byexposing the substrate to solutions of liposomes made up of lipidcomponents. Lipid bilayers and monolayers are well known.

Suitable phospholipids have a moiety that includes a charged phosphategroup forming the hydrophilic head, and one or more fatty acid residuesforming the hydrophobic tail. One group of phospholipids is derivedchemically from fatty triglycerides by replacing one of the three fattyacid residues with a phosphate group. The phosphate group can be furtheresterified with functionalizing molecules.

Replacing one of the fatty acid residues on a triglyceride with aphosphate group results in the formation of a phosphatide. Thediacylglycerol phosphate formed by a simple substitution of thephosphate for one of the acyl groups is called a phosphatidic acid. Ifthe phosphatidic acid is esterified in turn, the phospholipid is aphosphatidyl lipid. Examples include phosphatidyl choline, phosphatidylethanolamine, phosphatidyl serine, phosphatidyl glycerol, and the like.

Phospholipids of the phosphatidic acid and phosphatidyl series are namedas glycerol derivatives, naming the acyl or fatty acid group on the oneand two hydroxyls of the parent glycerol, with the phosphate or thephosphatidyl group provided at position three of glycerol. Normally twoof the three glycerol positions are esterified with fatty acids. In thelysophosphatidyl phospholipids (such as those exemplified in the Table),only the 1 position has a fatty acid moiety, with the phosphatecontaining group located on the 3-position.

Non-limiting examples of phospholipids in these classes are given in thefollowing table, which illustrates the naming convention and the genericnames of the various classes of phospholipid.

TABLE Representative Phospholipids Abbreviation CAS Name Type DDPC3436-44-0 1,2-Didecanoyl-sn-glycero-3- Phosphatidylcholinephosphocholine DEPA-NA 80724-31-8 1,2-Dierucoyl-sn-glycero-3-phosphatePhosphatidic acid (Sodium Salt) DEPC 56649-39-91,2-Dierucoyl-sn-glycero-3- Phosphatidylcholine phosphocholine DEPE988-07-2 1,2-Dierucoyl-sn-glycero-3- Phosphatidylethanolaminephosphoethanolamine DEPG-NA 1,2-Dierucoyl-sn-glycero-3[Phospho-Phosphatidylglycerol rac-(1-glycerol . . . ) (Sodium Salt) DLOPC998-06-1 1,2-Dilinoleoyl-sn-glycero-3- Phosphatidylcholinephosphocholine DLPA-NA 1,2-Dilauroyl-sn-glycero-3-phosphate Phosphatidicacid (Sodium Salt) DLPC 18194-25-7 1,2-Dilauroyl-sn-glycero-3-Phosphatidylcholine phosphocholine DLPE 1,2-Dilauroyl-sn-glycero-3-Phosphatidylethanolamine phosphoethanolamine DLPG-NA1,2-Dilauroyl-sn-glycero-3[Phospho- Phosphatidylglycerol rac-(1-glycerol. . . ) (Sodium Salt) DLPG-NH4 1,2-Dilauroyl-sn-glycero-3[Phospho-Phosphatidylglycerol rac-(1-glycerol . . . ) (Ammonium Salt) DLPS-NA1,2-Dilauroyl-sn-glycero-3- Phosphatidylserine phosphoserine (SodiumSalt) DMPA-NA 80724-3 1,2-Dimyristoyl-sn-glycero-3- Phosphatidic acidphosphate (Sodium Salt) DMPC 18194-24-6 1,2-Dimyristoyl-sn-glycero-3-Phosphatidylcholine phosphocholine DMPE 988-07-21,2-Dimyristoyl-sn-glycero-3- Phosphatidylethanolaminephosphoethanolamine DMPG-NA 67232-80-81,2-Dimyristoyl-sn-glycero-3[Phospho- Phosphatidylglycerolrac-(1-glycerol . . . ) (Sodium Salt) DMPG-NH41,2-Dimyristoyl-sn-glycero-3[Phospho- Phosphatidylglycerolrac-(1-glycerol . . . ) (Ammonium Salt) DMPG-NH4/NA1,2-Dimyristoyl-sn-glycero-3[Phospho- Phosphatidylglycerolrac-(1-glycerol . . . ) (Sodium/ Ammonium Salt) DMPS-NA1,2-Dimyristoyl-sn-glycero-3- Phosphatidylserine phosphoserine (SodiumSalt) DOPA-NA 1,2-Dioleoyl-sn-glycero-3-phosphate Phosphatidic acid(Sodium Salt) DOPC 4235-95-4 1,2-Dioleoyl-sn-glycero-3-Phosphatidylcholine phosphocholine DOPE 4004-5-1-1,2-Dioleoyl-sn-glycero-3- Phosphatidylethanolamine phosphoethanolamineDOPG-NA 62700-69-0 1,2-Dioleoyl-sn-glycero-3[Phospho-rac-Phosphatidylglycerol (1-glycerol . . . ) (Sodium Salt) DOPS-NA70614-14-1 1,2-Dioleoyl-sn-glycero-3- Phosphatidylserine phosphoserine(Sodium Salt) DPPA-NA 71065-87-7 1,2-Dipalmitoyl-sn-glycero-3-Phosphatidic acid phosphate (Sodium Salt) DPPC 63-89-81,2-Dipalmitoyl-sn-glycero-3- Phosphatidylcholine phosphocholine DPPE923-61-5 1,2-Dipalmitoyl-sn-glycero-3- Phosphatidylethanolaminephosphoethanolamine DPPG-NA 67232-81-91,2-Dipalmitoyl-sn-glycero-3[Phospho- Phosphatidylglycerolrac-(1-glycerol . . . ) (Sodium Salt) DPPG-NH4 73548-70-61,2-Dipalmitoyl-sn-glycero-3[Phospho- Phosphatidylglycerolrac-(1-glycerol . . . ) (Ammonium Salt) DPPS-NA1,2-Dipalmitoyl-sn-glycero-3- Phosphatidylserine phosphoserine (SodiumSalt) DSPA-NA 108321-18-2 1,2-Distearoyl-sn-glycero-3-phosphatePhosphatidic acid (Sodium Salt) DSPC 816-94-41,2-Distearoyl-sn-glycero-3- Phosphatidylcholine phosphocholine DSPE1069-79-0 1,2-Distearoyl-sn-glycero-3- Phosphatidylethanolaminephosphoethanolamine DSPG-NA 67232-82-01,2-Distearoyl-sn-glycero-3[Phospho- Phosphatidylglycerolrac-(1-glycerol . . . ) (Sodium Salt) DSPG-NH4 108347-80-41,2-Distearoyl-sn-glycero-3[Phospho- Phosphatidylglycerolrac-(1-glycerol . . . ) (Ammonium Salt) DSPS-NA1,2-Distearoyl-sn-glycero-3- Phosphatidylserine phosphoserine (SodiumSalt) Egg Sphingomyelin empty Liposome EPC Egg-PC PhosphatidylcholineHEPC Hydrogenated Egg PC Phosphatidylcholine HSPC High purityHydrogenated Soy PC Phosphatidylcholine HSPC Hydrogenated Soy PCPhosphatidylcholine LYSOPC MYRISTIC 18194-24-6 1-Myristoyl-sn-glycero-3-Lysophosphatidylcholine phosphocholine LYSOPC PALMITIC 17364-16-81-Palmitoyl-sn-glycero-3- Lysophosphatidylcholine phosphocholine LYSOPCSTEARIC 19420-57-6 1-Stearoyl-sn-glycero-3- Lysophosphatidylcholinephosphocholine Milk Sphingomyelin 1-Myristoyl-2-palmitoyl-sn-glycero 3-Phosphatidylcholine MPPC phosphocholine MSPC1-Myristoyl-2-stearoyl-sn-glycero-3- Phosphatidylcholine phosphocholinePMPC 1-Palmitoyl-2-myristoyl-sn-glycero-3- Phosphatidylcholinephosphocholine POPC 26853-31-6 1-Palmitoyl-2-oleoyl-sn-glycero-3-Phosphatidylcholine phosphocholine POPE1-Palmitoyl-2-oleoyl-sn-glycero-3- Phosphatidylethanolaminephosphoethanolamine POPG-NA 81490-05-3 1-Palmitoyl-2-oleoyl-sn-glycero-Phosphatidylglycerol 3[Phospho-rac-(1-glycerol) . . . ] (Sodium Salt)PSPC 1-Palmitoyl-2-stearoyl-sn-glycero-3- Phosphatidylcholinephosphocholine SMPC 1-Stearoyl-2-myristoyl-sn-glycero-3-Phosphatidylcholine phosphocholine SOPC1-Stearoyl-2-oleoyl-sn-glycero-3- Phosphatidylcholine phosphocholineSPPC 1-Stearoyl-2-palmitoyl-sn-glycero-3- Phosphatidylcholinephosphocholine

Another class of phospholipids that form bilayers is the sphingolipids.Sphingomyelin is a class of sphingolipids that has a phosphocholine orphosphoethanolamine molecule with an ester linkage to the one hydroxygroup of a ceramide. A ceramide in turn consists of a fatty acid chainattached through an amide linkage to sphingosine. An exemplary structureof a sphingolipid is

wherein R is the phosphorocholine or phosphoroethanolamine group. Thesphingolipids can vary with the structure of the fatty acid, which isshown in the Figure as a C₁₇ saturated fatty acid.

Lipid Anchored Ligands

The preferred phospholipids and sphingolipids self-assemble onto thesubstrate as a bilayer or monolayer when a substrate is exposed to asolution or suspension of liposomes made from the respectivephospholipids. The liposomes in turn self-assemble in solution when thecomponent lipids are dissolved in an aqueous system. If desired, a lipidmolecule containing a ligand (also called a “liganded phospholipid”) isalso provided in the solution from which the liposomes are produced.When assembled onto the substrate surface in a bilayer, this provides alipid anchored ligand in the fluid wall. In certain embodiments, theligand of the liganded phospholipid serves to bind or otherwise interactwith biomolecules or other analytes of interest.

The phospholipid derivatized with the ligand is provided in a suitablemole fraction relative to the other phospholipids. Normally, the molefraction of the liganded phospholipid is 0.5 or less, and above0.000001. Depending on the specificity and binding constant of theligand for the biomolecule, the mole fraction of ligand in the bilayercan be at least 0.000001, at least 0.00001, at least 0.0001, at least0.001, or at least 0.01 (the numbers are mole fractions ranging fromzero to one. A mole percent ligand can be derived by multiplying themole fraction by 100). In various embodiments, the mole fraction ofliganded phospholipid is no more than 0.5, no more than 0.2, no morethan 0.1, no more than 0.01, and no more than 0.001. Typical ranges ofmole fraction for the liganded phospholipid in the fluid lipid walls are0.000001-0.2, 0.00001-0.2, 0.001-0.1, 0.01-0.1, 0.000001-0.1,0.00001-0.1, 0.000001-0.01, 0.000001-0.001, and so on. In a preferredembodiment, the ligand is covalently attached to a structure like thatof the other phospholipids in the bilayer. For example, a ligandingfunctional group such as biotin can be covalently attached to thenitrogen of a phosphatidylethanolamine molecule. Many other examples areknown or can be synthesized.

The ligand to be incorporated into the bilayer to provide the lipidanchored ligand of the invention is selected from compounds that have awide range of functional groups. Basically, any functional group towhich the biomolecule of interest will bind or link to covalently can beused. For any ligand/biomolecule combination, suitable conditions can beempirically determined. Generally, the stronger the affinity of theligand and biomolecule (expressed in the conventional way as bindingconstants or inhibition constants), the lower the mole fraction need beprovided of the ligand in the fluid wall. The converse is also true inthat the weaker the affinity of the ligand and biomolecule interaction,the higher the mole fraction need be provided of the ligand in the fluidwall. A quick calculation suggests that ˜20 mM will be the weakestequilibrium dissociation constant (Kd) that the system will work withfor detecting specifically lipid-attached proteins. Stronger affinities(Kd<20 mM) will allow the system to use less ligand in the fluid walls.

The nature of the ligand and its concentration in the bilayer can bevaried to provide a suitable amount of binding in the fluid wall liningthe nanopore. Although the invention is not limited by theory, thisaffinity of the biomolecule for the ligand in the fluid wall or thecovalent bond of a biomolecule to a lipid in the fluid wall accounts forat least some of the advantages provided by the method. In particular,it is believed that binding to these ligands or covalent bond to a lipidin fluid wall effectively anchors the protein to a lipid in the fluidwall and slows down the translocation of the biomolecule through thenanopore, thereby allowing the electronics to time resolve thetranslocation events.

Examples of Ligands

Examples of ligands that can be covalently incorporated into thephospholipid bilayers as discussed above include biotin, cholesterol,sulfonamide, nickel (coupled with nickel chelating lipids) andantibodies. Other examples of ligands include proteins. In variousembodiments proteins used as ligands contain functional groups or can bemodified to contain functional groups that can react for covalentattachment. Examples of such groups on proteins include thiol groups,maleimide groups, N-hydroxysuccimide (NHS) ester groups, or so called“Click” chemistry, which proceeds through nitrile, acetylene, or azidegroups, or cycloadditions such as the Diels Alder reaction.

Manufacture of Nanopores

The nanoholes can be fabricated in materials such as silicon nitride,silicon dioxide, borosilicate glass, aluminum oxide, or polyethyleneterephthalate. Depending on the material and the size of the desiredhole, different fabrication techniques are used. Common techniquesinclude the so called “track etching technique” (Harrell, C. C. et al.,(2003), Synthetic single-nanopore and nanotube membranes, Anal. Chem.75:6861-6867), the “ion beam sculpting” technique (Jiali Li et al.,(2001), Ion Beam Sculpting at nanometer length scales, Nature 412,166-169), the “electron beam sculpting” technique (Storm, A. J. et al.,(2003), Fabrication of solid-state nanopores with single-nanometerprecision, Nat. Mater. 2:537-540), and “the laser machining in glass”technique (Joglekar et al. (2004), Optics at critical intensity:applications to nanomorphing, PNAS, 101: 5856-5861).

When the lipid bilayer is formed in the passageway of the substrate, theeffective dimension or diameter of the passageway is reduced by thethickness of the bilayers formed. One speaks then of a nanopore having anominal dimension that takes into account the lowering of the effectivediameter of the passageway as a consequence of the bilayer being formed.Normally the nominal diameter or dimension of the nanopore is thedimension of the passage or hole through the substrate reduced by twotimes the bilayer thickness plus a layer of water between the lipidbilayer and the substrate surface or one time a monolayers thickness. Ifthe passageway is perfectly round, diameter and dimension are usedinterchangeably. For shapes other than round, other dimensions can beused, such as chords, long axes, short axes, and the like. Frequently,the dimension of interest is the nominal dimension of the nanopore thatpermits a non-spherical biomolecule to pass through, in some orientationwhere the dimension of the biomolecule and the pore are in relation toone another.

The nominal dimension of the nanopore, being a function of the bilayerthickness, is therefore also a function of the length of the “tail” (theacyl chains) on the phospholipids in the bilayer, since the thickness ofthe bilayer depends on the tail length. The length of the tail in turndepends on the number of carbon atoms and the number of double bonds.These features are illustrated further in the Examples section below. Incertain embodiments, the nominal dimension of the nanopores can befine-tuned by the choice of phospholipid.

Biomolecules

Using the methods and devices described herein, a variety ofbiomolecules can be detected and studied. Generally speaking, anymolecule or particle having nanometer dimensions can be studied. Theseinclude biomolecules such as proteins, nucleic acids, antibodies,polysaccharides, virus capsids, biopolymers such as fibrils and so on aswell synthetic particles such as polystyrene particles, goldnanoparticles, or dendritic particles. Additional subjects of studyinclude protein aggregates such as those formed by amyloid beta (Aβ)peptides. Other aggregates include immune complexes and G-proteincoupled receptors. By using the nanopores with fluid walls,translocation times of such molecules or particles through nanopores isslowed down sufficiently that the transit or translocation events can beisolated and measured.

Further non-limiting description is provided in the following Examplessection. The Examples present enabling disclosure for carrying out theinvention.

EXAMPLES

Nanopores hold tremendous promise for applications such assingle-molecule binding assays¹⁻³, portable detection of (bio)warfareagents⁴⁻⁶, and ultra-fast sequencing of DNA or RNA^(7,8). Nanopore-basedexperiments provide sub-molecular detail on the composition ofindividual molecules⁹ and on the formation of molecular complexes oraggregates^(1,10). Recording of resistive current pulses during thetranslocation of single molecules through electrolyte-filled nanoporesmakes it possible to study their size^(1,4,6,11-13),conformation^(14,15), and activity^(16,17) in situ^(3,18-23). Thistechnique can characterize hundreds of unlabeled single molecules persecond in physiological solutions and yields distributions of measuredparameters from these single-molecule investigations^(3,9). However,several challenges should be addressed. First, there is a need formethods that can reliably fabricate synthetic nanopores on thesub-nanometer scale²⁴ and adjust or actuate pore diameters insitu^(24,25). Second, better control of translocation times ofsingle-molecule analytes are still needed to achieve complete timeresolution of translocation signals and more accurate determination ofthe amplitude and duration of resistive pulses²⁶⁻²⁸. Third, methods tocontrol the surface chemistry inside synthetic pores¹⁶ may reducenon-specific interactions of analytes with the pore walls^(1,3,29) andprevent pore clogging³. Finally, low frequency of translocation eventsat low analyte concentrations³⁰ and the poor specificity of thenanopores for analytes³ need to be improved.

Nature solved most of these challenges in the design of biologicalnanopores²³. Ion channel proteins, for instance, fold intothree-dimensional structures with predetermined locations of individualatoms and precisely defined internal diameters that can be actuated byligand binding or by changes in the environment of the pore³¹. Many ionchannel proteins are specific towards ligands and permeants, haveminimal non-specific interactions, and irreversible clogging is rare.However, instability of these proteins limits their sensingapplications²³.

Insects detect pheromones by translocating odorant molecules throughlipid-coated nanopores (diameter 6-65 nm) that span their exoskeleton(FIG. 1a )³²⁻³⁴. These lipid coatings are thought to participate incapture, pre-concentration, and subsequent translocation of odorants tospecific receptors on dendrites of olfactory neurons in the antennae ofinsects^(32,34). Inspired by this design, we explored whether coatingsynthetic nanopores of comparable diameters with fluid lipid bilayerscould provide benefits for nanopore-based, resistive pulse sensing ofsingle proteins while addressing the associated challenges. Coatingsynthetic nanopores with organic molecules has been shown but thesecoatings were fixed on the surface of the pore³⁵⁻³⁷. Here we introducethe concept of fluid coatings

Methods Lipids and Proteins

We obtained all phospholipids from Avanti Polar Lipids, Inc. Wepurchased the proteins streptavidin (SA) and monoclonal anti-biotinantibody (mAb, B7653) from Sigma Alrdrich and polyclonal anti-biotin Fabfragments (Fab, 20938) from Rockland Inc.

Nanopores

We used a focused ion beam to fabricate nanopores in a silicon nitridemembrane that was supported by a silicon chip (see Supplementary SectionS1 for information on the pores)⁵⁹. Prior to experiments, we cleaned thepore-containing chips for at least 30 min with a fresh mixture of 3:1(v/v) concentrated sulfuric acid and 30% (v/v) aqueous hydrogen peroxidesolution at a temperature of 60-70° C. followed by rinsing withdeionized water and drying with argon gas. To create separate fluidcompartments on either side of the nanopore, we mounted the chip betweentwo pieces of cured polydimethylsiloxane (PDMS)¹⁰. After eachexperiment, we rinsed the silicon chips for 2-3 min successively withthe following solvents: water, ethanol, methanol, and chloroform. Westored chips in chloroform between experiments.

Formation of Supported Lipid Bilayers

We formed supported lipid bilayers by fusion of small unilamellarvesicles (SUVs)⁴⁰⁻⁴³. We prepared these SUVs as described inSupplementary Section S2. To form the supported lipid bilayer on siliconnitride membranes, we filled the top compartment of the PDMS fluidicsetup with 10-30 μL of the aqueous solution with the SUVs and the bottomcompartment with a 150 mM KCl solution without liposomes. After 5-10min, we removed excess SUVs by immersing the entire fluidic setup for5-10 min in a large (500 mL) beaker containing deionized water. Beforerecordings, the fluidic compartments were filled with the desiredelectrolyte. Each liposome preparation contained 0.8 mol % of thefluorescently-labeled lipid,1,2-dipalmitoyl-sn-glycero-3-phosphoethanolamine-N-(lissamine rhodamineB sulfonyl) (Rh-PE), for measuring the fluidity of lipid bilayers byfluorescence recovery after photobleaching (FRAP, see SupplementarySection S2).

Electrical Resistance as a Function of Bilayer Thickness

We used Ag/AgCl pellet electrodes (Warner Instruments) to monitor ioniccurrents through electrolyte-filled nanopores with a patch-clampamplifier (Axopatch 200B, Molecular Devices Inc.) in voltage clamp mode(i.e., at constant applied voltage). See Supplementary Section S9 for adescription of data acquisition methods. We determined the resistancebetween the electrodes by measuring the current at various appliedvoltages in the range of ±0.5 V; the slope of the corresponding currentversus voltage plots equaled the inverse of the resistance. To measurethe resistance as a function of the bilayer thickness, we formeddifferent lipid bilayers on the same chip by using SUVs composed ofDLPC, DMPC, DΔPPC, or DEPC lipids. We cleaned this chip before theformation of each lipid bilayer as described above. The chip used forthese experiments contained a nanopore with a diameter of 28 nm and alength of 12 nm (see Supplementary Section S1 for a TEM image) and therecording buffer contained 500 mM KCl and 10 mM HEPES at a pH value of7.4±0.1. To measure the resistance of nanopores as a function oftemperature, we used a feedback-controlled Peltier Cooler from WarnerInstruments (see Supplementary Section S1).

Sensing Proteins with Biotinylated Lipids in the Bilayer

We formed supported lipid bilayers on the silicon chip from SUVscontaining 0.15-0.4 mol % of biotin-PE, 0.8 mol % Rh-PE, and ˜99 mol %POPC. We used an electrolyte containing 2.0 M KCl and 10 mM HEPES with apH of 7.4±0.1 and performed all current recordings at −0.1 V. To detectSA, we used a nanopore with an area-equivalent diameter of 19.2 nm (seeSupplementary Section S1) and a length of 18 nm (before formation of thebilayer), and we added SA to the top compartment at concentrations of3.2-6.2 pM. To detect mAb and Fab, we used a nanopore with an areaequivalent diameter of 33.0 nm and a length of 22 nm; we added mAb orFab to the top compartment at concentrations of mAb or Fab of 0.1-50 nM.(See Supplementary Section S9 for a description of the resistive-pulseanalysis.)

Detection of Aggregates of Amyloid-Beta (Aβ) Peptides

See Supplementary Section S10 for a description of Aβ samplepreparation. We used a nanopore with a diameter of 96 nm and a length of˜275 nm (before bilayer coating), which was either uncoated or coatedwith a POPC bilayer. We added solutions containing Aβ peptides (residues1-40) to the top compartment at concentrations of Aβ of 0.1 to 0.2mg×mL⁻¹. We used an electrolyte containing 70 mM KCl and 10 mM HEPESwith a pH of 7.4±0.1 and recorded resistive pulses at +0.2 V.

Example 1 Bilayer Coatings Enable Fine Tuning and Actuating PoreDiameters

To create lipid bilayer-coated nanopores (FIG. 1b ), we exposed siliconchips that contained a single pore through a silicon nitride window toan aqueous suspension of small unilamellar liposomes⁴⁰⁻⁴³. Spreading ofthese liposomes on the Si₃N₄ window and on the walls of the nanopore(see Supplementary Sections S1-S3) created a bilayer coating and reducedthe nanopore diameter. The thickness and surface chemistry of thiscoating can be accurately controlled by the choice of lipids in theliposome preparation. For instance, the bilayer thickness is fine-tunedby the length and the number of double bonds in the hydrocarbon tails ofthe lipids (FIG. 1c ), whereas the surface chemistry is controlled bythe nature of their polar head groups (see Supplementary Section S4).

The capability of fine-tuning the diameter of nanopores is illustratedby the red curve in FIG. 1c . This curve resulted from a best fit of thedata to a simple physical model that described the electrical resistancethrough the nanopore, R (a), as the sum of four terms: 1) the resistanceof the cylindrical nanopore, 2) the access resistance to and from thenanopore³¹, 3) the resistance of the cylindrical channel through thesilicon nitride window that led to the pore (see Supplementary SectionS1 for a schematic drawing), and 4) the access resistance to thiscylindrical channel. These four resistances in series are represented insequence by the terms in equation (1) (see Supplementary Section S1 fora derivation):

$\begin{matrix}{{R = {\frac{\rho \left( {l_{p} + {2d} + {2w_{L}}} \right)}{{\pi \left( {r_{P} - d - w_{L}} \right)}^{2}} + \frac{\rho}{2\left( {r_{P} - d - w_{L}} \right)} + \frac{\rho \left( {l_{C} + {2d} + {2w_{L}}} \right)}{{\pi \left( {r_{C} - d - w_{L}} \right)}^{2}} + \frac{\rho}{4\left( {r_{C} - d - w_{L}} \right)}}},} & (1)\end{matrix}$

where ρ (Ω m) represents the resistivity of the electrolyte, l_(P) (m)the length of the cylindrical nanopore, d (m) the thickness of the lipidbilayer (see Table 1), w_(L) (m) the thickness of the interstitial waterlayer between the bilayer and the silicon nitride wall of thepore^(44,45), r_(P) (m) the radius of the nanopore, l_(C) (m) the lengthof the cylindrical channel through the silicon nitride that led to thepore, and r_(C) (m) the radius of this cylindrical channel (seeSupplementary Section S1 for values of ρ, l_(P), r_(P), l_(C), andr_(C)).

TABLE 1 Lipids used in this work to coat nanopore walls. BilayerAbbrevia- Acyl Thickness^(b) Chemical Name tion Chains^(a) (nm)1,2-dilauroyl-sn-glycero-3- DLPC (12:0) 3.0 ± 0.1 phosphocholine1,2-dimyristoyl-sn-glycero-3- DMPC (14:0) 3.4 ± 0.1 phosphocholine1,2-dipalmitoleoyl-sn-glycero-3- D□PPC (16:1) 3.6 ± 0.1 phosphocholine1,2-dieicosenoyl-sn-glycero-3- DEPC (20:1) 4.2 ± 0.1 phosphocholine1-palmitoyl-2-oleoyl-sn-glycero-3- POPC (18:1- 3.7 ± 0.1 phosphocholine16:0) 1,2-dipalmitoyl-sn-glycero-3- biotin-PE (16:0) —phosphoethanolamine-N-(cap biotinyl) ^(a)For lipids with two identicalacyl chains, (c:db) indicates the number of carbons (c) and the numberof double bonds (db); for lipids with two different acyl chains,(c1:d1-c2:db2) refer to acyl chains 1 and 2. ^(b)Thickness according toLewis et a1³⁸.

Equation (1) shows that this model estimated the effective, open radiusof a pore by taking into account the reduction of its radius andincrease of its length as a function of the thickness of the bilayercoating and the thickness of the interstitial water layer between thebilayer and the silicon nitride wall of the pore. A fit of the data inFIG. 1c to this model returned a thickness of the water layer ofw_(L)=1.2±0.1 nm (literature values: 0.5-1.7 nm)^(44,45) as the onlyfitting parameter. The excellent fit of the data to equation (1)(R²=0.97, N=7) and the realistic value for the thickness of the waterlayer, suggest that self-assembled bilayer coatings make it possible tofine-tune and predict the radius of a cylindrical nanopore in incrementsof two carbon atoms (albeit in a range limited to lipids that cangenerate stable supported lipid bilayers).

Since the sensitivity and information content of nanopore-basedsingle-molecule experiments depend strongly on the size of the pore, oneparticularly desirable feature for nanopore sensing would be the abilityto adjust the diameter of a nanopore dynamically to the size of variousanalytes, in situ. FIG. 1d demonstrates that a thermal phase transitionof a coating of DMPC lipids (Table 1) from the ordered gel phase (L_(β))to the disordered liquid crystalline phase (L_(β)) decreased theestimated thickness of the bilayer coating by Δd≈0.7 nm (lit.: 0.9-1.1nm)^(39,46,47) and made it possible to actuate the diameter of thenanopores dynamically by 1.4±0.1 nm. FIG. 1d also shows that themidpoint (dashed blue line) and range (grey area) of the phasetransition in the nanopore coating occurred precisely at the reportedtemperature for DMPC lipids of 23.5±2.3° C.³⁹. Changing the diameter ofnanopores by a phase transition of lipids may be a relevant mechanism bywhich insects regulate their water uptake and evaporative loss throughlipid-coated nanopores in their exoskeleton^(34,48). In the context ofsynthetic nanopores, this bio-inspired capability of changing porediameters constitutes a novel approach to determine thermal phasetransition temperatures of lipid bilayers, in situ.

Example 2

Lipid Anchored Ligands Concentrate Specific Analytes and Enable theirTranslocation

In addition to fine-tuning and actuating the diameters of nanopores,bilayer coatings provide a straightforward strategy to render nanoporerecordings specific for certain analytes by functionalizing the bilayersurface with ligands or receptors. FIG. 2 illustrates that addingdefined mole fractions of lipids with desired functional groups (here,biotinylated lipids) during the formulation of liposomes and thesubsequent formation of a bilayer coating⁴² can control the surfacedensity of ligands in and around the pore. These lipid-anchored ligands,which were mobile within the fluid sheet of the lipid bilayer, couldconcentrate dilute analytes from the bulk solution to specific ligandson the bilayer surface and deliver these analytes to the pore bytwo-dimensional diffusion (FIG. 2a,b ). Compare the lipid coating ofolfactory sensilla in insect antenna, which contributes to the extremelysensitive detection of lipophilic pheromones by insects^(32,34,49).

Pre-concentrating and translocating analytes that are bound to a fluidsurface also made it possible to distinguish between different analytesbased on their affinity to the displayed ligand (FIG. 2c ). Forinstance, proteins present at picomolar concentrations in the bulkelectrolyte solution concentrated at the surface and induced frequenttranslocation events if they bound with high affinity to lipid-anchoredligands in the bilayer. In contrast, proteins with low affinity to theseligands required more than 300-fold increased bulk concentrations toreach comparable frequencies of time-resolved translocation events (FIG.2c ). In the case of streptavidin, polyclonal anti-biotin Fab fragmentsand monoclonal anti-biotin IgG antibodies, we found that to reach afrequency of 30-100 translocation events per second, a concentration ofonly 0.006 nM streptavidin was required compared to 1 nM of Fab fragmentand 20 nM monoclonal antibody. Control experiments revealed that in theabsence of biotinylated lipids in the bilayer coating, or in thepresence of excess biotin in solution, the frequency of detectabletranslocation events for each protein was up to 500-fold lower than inthe presence of specific capture sites in the bilayer (FIG. 2b andSupplementary Section S5).

Example 3 Bilayer Viscosity Controls and Prolongs Translocation ofLipid-Anchored Analytes

The capability of moving captured analytes through pores with fluidwalls made it possible to obtain the translocation time, t_(d), throughthe pore as well as the corresponding amplitude of the resistive pulses,ΔI. This information is unique to the fluid nanopore coatings introducedhere; previous reports on nanopore recordings with specific,surface-attached binding groups captured analytes on permanently fixedpositions4,5 and did not allow translocation of bound analytes therebyexcluding the possibility to determine t_(d) or to relate ΔI to themolecular volume of the bound analyte. An additional benefit oftranslocating analytes that are bound to a lipid anchor emerges if theintrinsic translocation speed of the unbound analyte through a pore istoo fast to resolve t_(d) and ΔI completely in time—a problemencountered previously by other groups26-28.

FIG. 2b and Supplementary Section S5 show that translocation events ofindividual proteins could not be fully resolved without lipid-anchoredcapture sites. In contrast, anchoring analytes to lipids during theirpassage through the pore had the advantage that the translocation speedwas dominated by the high viscosity of the bilayer coating rather thanthe low viscosity of the aqueous electrolyte in the pore50. Theresulting, prolonged translocation times enabled time-resolved detectionof t_(d) (FIG. 3) and ΔI (FIG. 4) combined with accurate, quantitativecharacterization of individual proteins. Alternative strategies forprolonging the translocation time by increasing the length of the poreor the viscosity of the electrolyte or by reducing the applied voltagehave been associated with a reduction of the amplitude of translocationevents and reduced the signal to noise ratio28. In contrast, bilayercoatings with fluid capture sites can fine-tune the viscosity of thebilayer and prolong the translocation times of lipid-anchored analyteswhile the conductivity of the aqueous electrolyte remains unchanged.

FIG. 3a demonstrates that acyl chains with increasing length andsaturation could slow down translocation speeds. For instance, POPClipids with one monounsaturated acyl chain of 18 carbon atoms and asecond saturated acyl chain of 16 carbons generated approximately 1.4times more viscous bilayers than DΔPPC lipids with two monounsaturatedacyl chains of 16 carbons. These two bilayer coatings resulted in mostfrequently observed translocation times for streptavidin of 114±15 □s inthe POPC coating compared to 81±10 μs in the DΔPPC coating (FIG. 3a ).Translocation speeds could be slowed down even further by adding 50 mol% cholesterol to a POPC bilayer; in this case the most frequentlyobserved translocation time of Fab fragments doubled from 78±5 μs to175±4 μs (FIG. 3b ).

Example 4 Resolving Translocation Events Enables Determining the Volumeof Individual Proteins

Complete time resolution of translocation events of lipid-anchoredproteins allowed us to determine the volume of individual translocatingproteins based on accurate acquisition of the amplitude of resistivepulses, ΔI(t). FIG. 4 shows amplitude distributions of the resistivepulses for three different biotin-binding proteins. We used equation (2)to estimate the transiently excluded volume of electrolyte, Λ(t) (m³)during the translocation of these three proteins12,13,51.

$\begin{matrix}{{\Delta \; {I(t)}} = {\frac{\gamma \; V_{a}{\Lambda (t)}}{{\rho \left( {l_{P} + {1.6r_{P}}} \right)}^{2}}{S\left( \frac{r_{P}}{d_{M}} \right)}}} & (2)\end{matrix}$

In this equation, γ (unitless) represents a shape factor52 with a valueof 1.5 for spheres, Va (V) is the total applied voltage, and S(rP/dM) isa correction factor that depends on the relative values of rP and thediameter of the molecule, dM. Like most groups, we used a value of 1 forS(rP, dM) for all calculations12,13. Since Λ(t) from the translocationof spheroidal particles is approximately equal to the molecular volumeof the particles14,29, we were able to estimate the molecular volumes ofstreptavidin (94±18 nm3; lit. value: 105±3 nm3)53, Fab fragments (172±31nm3; lit. value: ˜140 nm3)54, and antibodies (308-696 nm3; lit. value:347±15 nm3)55. The distributions of ΔI values for streptavidin (FIG. 4a) and Fab fragments (FIG. 4b ) were significantly narrower than thedistribution for the antibodies (FIG. 4c ). Since control experimentsrevealed that the broad distribution was not caused by contamination ofthe antibody sample with other proteins (see Supplementary Section S6),we attribute the broad distribution of ΔI values in FIG. 4c primarily tothe complex molecular shape of IgG antibodies (γ≠1.5) compared to theapproximately spherical shape (γ≈1.5) of streptavidin and Fab fragments(for a detailed discussion on the proposed effect of molecular shape onΔI, see Supplementary Section S6).

Example 5 Determining Translocation Time and Charge of DifferentProteins

FIG. 3 shows that different proteins moved through the nanopores atdifferent, truly distributed speeds as expected for biased diffusionfirst passage time processes14. Because we performed the experimentswith streptavidin using a different pore (see Supplementary Table 51 fordimensions of pores used for all experiments), a direct comparison ofthe most frequently observed td values was only possible between Fabfragments (78±5 μs, blue bars in FIG. 3b ) and monoclonal antibodies(54±8 μs; FIG. 3c ). The observed differences in td values added a thirddimension for distinguishing between different proteins in addition tocomparing their affinity to specific ligands based on the frequency oftranslocation events (FIG. 2c ) and quantifying their molecular volumesbased on ΔI values (FIG. 4a-c ).

Since the translocation speed of different lipid-anchored proteinsvaried, we hypothesized that the fluid nature of the pore walls mayminimize non-specific adsorption processes and open the door todetermining the net charge of proteins. To test this hypothesis, wedeveloped the simplest possible model that yields a relationship betweentd of a lipid-anchored protein and the net charge of this protein,|z|×e, based on a model introduced recently by Sexton et al26. Here z(unitless) is the net valency of the overall charge on the protein and e(C) is the elementary charge of an electron. This model assumed that acharged protein experiences an electrophoretic force that is opposed bythe viscous drag inside the pore and leads to a constant drift velocity(lP/td) through the pore. It also assumed that the viscous drag oflipid-anchored proteins is determined by the diffusion constant of thelipid anchor, DL (m2 s-1) in the lipid bilayer rather than by thediffusion constant of the protein in the aqueous electrolyte inside thepore lumen50. Based on these assumptions, we derived equation (3) topredict td values theoretically (for a detailed derivation andadditional assumptions made, see Supplementary Section S8):

$\begin{matrix}{t_{d} = \frac{l_{P}^{2}k_{B}T}{\left| z \middle| {e\; V_{P}D_{L}} \right.}} & (3)\end{matrix}$

Here kB (J K-1) is the Boltzmann constant, T (K) is temperature and Vp(V) refers to the part of the total applied voltage that drops insidethe pore; it does not include the voltage drop due to the accessresistance to and from the pore (see Supplementary Section S8).

Equation (3) made it possible to compare theoretically predicted tdvalues with experimentally determined values for proteins with known netcharge. FIG. 5 shows this comparison for translocation events ofstreptavidin at five different pH values in the recording electrolyteand therefore five different values of |z|. The excellent agreementbetween the data (black squares) and the predicted td values (red curve)supports the simple model used for the derivation of equation (3).

Additional support for this model stems from a comparison between twobilayer coatings of different viscosity. In one experiment we coated thenanopore with a POPC bilayer and in the other experiment with a DΔPPCbilayer. Before adding streptavidin to the top compartment of the chips,we determined the lateral diffusion coefficient of lipids in the POPCbilayer (DL=1.13±0.11 nm2 μs-1) and in the DΔPPC bilayer (DL=1.56±0.16nm2 μs-1) by fluorescence recovery after photobleaching (FRAP)experiments on the silicon nitride support (see Supplementary SectionS2)57. With these DL values and a valence of net charge of|z|=|−1.9±0.4| at pH 7.456, equation (3) predicted a translocation timefor streptavidin of 126±29 μs in POPC-coated pores and of 91±21 μs inDΔPPC-coated pores. Experimentally, the most frequently observedtranslocation time of streptavidin (FIG. 3a ) was 114±15 μs throughpores with a POPC coating (deviation from the predicted value: −10%) and81±10 μs through pores with a DΔPPC coating (deviation from thepredicted value: −11%). The excellent agreement between thetheoretically predicted values of td and the experimentally measured tdvalues as well as the data in Table 2 confirm that translocation timesof lipid-anchored analytes were indeed dominated by the viscosity of thebilayer50 and were hence independent of the shape of the proteins (FIG.3b,c ).

TABLE 2 Comparison of diffusion coefficients of lipid-anchored proteinswithin the nanopore, D_(P), with diffusion coefficients of lipids,D_(L), in coatings of two different lipid bilayers on three differentnanopores. Lipid D_(L) ^(b) D_(P) ^(c) ΔD Protein bilayer^(a) (nm² μs⁻¹)(nm² μs⁻¹) % SA^(d) DΔPPC 1.56 ± 0.16 1.7 ± 0.4 +9 SA^(d) POPC 1.13 ±0.11 1.2 ± 0.3 +6 SA^(e) POPC 1.65 ± 0.17 1.9 ± 0.5 +15 mAb^(f) POPC1.29 ± 0.13 2.6 ± 0.7 +100 Fab^(f) POPC 1.27 ± 0.13 1.5 ± 0.2 +18^(a)All lipid bilayers also contained 0.15-0.4 mol % of biotin-PE.^(b)Values for D_(L) were determined by FRAP as described inSupplementary Section S2. ^(c)Values for D_(P) were determined withequation (3) based on the most frequently measured values of t_(d) andvalues of |z| for SA from Sivasankar et al⁵⁶ and values of |z| for mAband Fab as determined by capillary electrophoresis (see SupplementarySection S8). ^(d)Nanopore dimensions: r_(P) = 10.0 nm, l_(P) = 18 nm^(e)Nanopore dimensions: r_(P) = 10.5 nm, l_(P) = 18 nm ^(f)Nanoporedimensions: r_(P) = 16.5 nm, l_(P) = 22 nm

These observations raise the possibility to use t_(d) values, in analogyto migration times in electrophoresis, for distinguishing between, andpossibly identifying, specific proteins. The agreement between theoryand experiment also suggests that determining translocation times oflipid-anchored proteins through a bilayer-coated nanopore makes itpossible to determine the net charge of proteins. For instance, at pH7.4, the measured t_(d) values suggest a net charge between −2.9 and−5.3 for the polyclonal anti-biotin Fab fragments and a net charge of−4.2±0.5 for the monoclonal anti-biotin antibodies (see SupplementarySection S8). These values agree well with results from capillaryelectrophoresis experiments (see Supplementary Section S8). Moreover,for a protein with known charge, translocation experiments combined withequation (3), make it possible to determine—non-optically—the lateraldiffusion constants of lipids and therefore the fluidity of bilayerswithin seconds (Table 2). This attribute might be useful to testtherapeutic compounds for their propensity to change membranefluidity⁵⁷.

Finally, the agreement between predicted and experimental t_(d) valuessuggests that the measured t_(d) values are close to the “true”electrophoretic translocation times. In other words, these measuredtranslocation times represent translocation in the absence ofnon-specific adsorption of proteins to the bilayer coating or to thesilicon nitride substrates. This point is important because allsingle-molecule translocation experiments with proteins reported so farwere hampered by non-specific adsorption of proteins to the nanoporewalls with regard to accurate determination of t_(d) values^(1,14,26).In some cases, these interactions increased the translocation times ofproteins by several orders of magnitude²⁶.

Example 6

Fluid Walls Translocate Aggregated Aβ Peptides without Clogging

Due to the unique capability of fluid bilayer coatings to eliminatenon-specific interactions, these pores made it possible to analyzetranslocation events of molecules that aggregate and have a tendency toclog nanopores. Amyloidogenic peptides, such as Alzheimer'sdisease-related amyloid-β (Aβ) peptides⁵⁸, belong to this category ofmolecules. The current versus time trace in FIG. 6a shows that ananopore without a bilayer coating clogged within minutes after additionof Aβ peptides. Despite several attempts, we were never able to detecttranslocation events from samples of Aβ peptides with uncoated pores. Incontrast, FIG. 6b illustrates that coating nanopores with bio-inspired,fluid lipid bilayers incurred non-fouling properties to these pores andmade it possible to detect numerous large amplitude translocation eventsdue to the passage of individual Aβ oligomers and fibrils.

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Example 7 Single Particle Characterization of Aβ Oligomers in Solution.

Here, we extend the use of lipid-coated nanopores from analyzing Aβfibers to characterizing the smaller and clinically more relevantsoluble oligomeric Aβ species. The lipid coating of the nanopore (FIG.8A inset) is required for detection of Aβ aggregates since nanoporeswithout the fluid coating clogged due to adsorption of Aβ on thenanopore walls (see Supporting Information S11).³⁵ We show thatresistive pulse sensing with lipid-coated nanopores can be used to trackthe time-dependent aggregation of Aβ₍₁₋₄₀₎ by monitoring thedistribution of Aβ aggregates in solution, and we validated this methodby analyzing transmission electron microscopy micrographs of Aβ₍₁₋₄₀₎aggregates.

To perform nanopore-based detection of Aβ₍₁₋₄₀₎ aggregates, we startedfrom aqueous solutions containing mostly Aβ₍₁₋₄₀₎ monomers (seeSupporting Information S12). We prepared aggregates of Aβ₍₁₋₄₀₎ byincubating these solutions for zero to three days before adding them tothe electrolyte in the top compartment of the recording setup (FIG.8A).^(20,52) We confirmed by gel electrophoresis that this preparationmethod resulted in increasing aggregate sizes over time (see SupportingInformation S13).⁵²

FIG. 8B shows recordings of the baseline current before and after addingAβ₍₁₋₄₀₎ solutions that had been permitted to aggregate for one andthree days. Consistent with time-dependent aggregation, the currenttrace from the three-day sample shows resistive pulses with increasedfrequency and larger amplitude than the current trace from the one-daysample. FIG. 9A shows scatter plots of ΔI versus t_(d) values fortranslocation events with a ΔI value greater than 250 pA (5 times thestandard deviation of the noise) and with a t_(d) value greater than 35μs (the smallest t_(d) value we can measure accurately).^(35,53) Asexpected, the values of ΔI, and hence the sizes of aggregates, increasedwith increasing aggregation time. Interestingly, the amplitude of ΔIvalues reached a maximum at ˜5 nA (˜10% of the baseline currentmagnitude), despite large variations in t_(d) values (FIG. 9B, clusteriv). This result is consistent with translocation of cylindrical objectswith similar diameters but varying lengths that are longer than thelength of the nanopore, since the sensing zone is limited to the volumeof the nanopore and its effective length. These characteristics apply toprotofibrils, which have lengths up to 200 nm, and fibers, which havecan reach lengths up several μm. Both types of aggregates have constantdiameters along their length, and therefore, resistive pulses due totheir translocation will have a maximum ΔI value but very distributedt_(d) values.^(8,21)

In order to distinguish among resistive pulses resulting from thetranslocation of spherical oligomers, protofibrils or fibers through thenanopore, we performed a cluster analysis on a data set from allresistive pulses (FIG. 9B) based on the ΔI and t_(d) value for eachtranslocation event. To perform the cluster analysis we used the Fuzzyalgorithm in the open-source, statistics software R and set the numberof clusters to four, since we expected four clusters of ΔI versus t_(d)values to emerge representing the translocation of: (i) sphericaloligomers, (ii) cylindrical protofibrils with lengths shorter than theeffective length of the nanopore, (iii) cylindrical protofibrils withlengths longer than the effective length of the nanopore, or (iv) fiberswith a length longer than the effective length of the nanopore. Thecolored points in FIG. 9B illustrate the resulting assignment given toeach recorded resistive pulse. FIG. 9B also reveals the expected resultthat clusters (iii) and (iv) contain resistive pulses with ΔI valuesthat converge at 1 to 2 nA and at 3 to 4 nA, respectively, while theirt_(d) values vary by four orders of magnitude (35 us to 100 ms),suggesting these clusters contain resistive pulses due to thetranslocation of protofibrils and fibers with lengths longer than thelength of the nanopore and with somewhat constant diameters.

To determine the size of Aβ₍₁₋₄₀₎ aggregates in each cluster, we usedthe value of ΔI from each translocation event and considered two extremecases yielding two different equations.^(35,47,57) Equation (3)describes the relationship between ΔI and the excluded volume, Λ(nm³),of spherical oligomers,⁵⁸⁻⁶¹ while equation (4) describes therelationship between ΔI and the average cross-sectional area, A_(X)(nm²), of aggregates with lengths longer than the effective length ofthe nanopore.^(57,62)

$\begin{matrix}{{\Delta \; I} = {{\frac{\gamma \; V_{A}\Lambda}{{\rho \left( {I_{P} + {1.6r_{P}}} \right)}^{2}}\mspace{14mu} {for}\mspace{14mu} I_{M}} < I_{eff}}} & (3) \\{{\Delta \; I} = {{\frac{\gamma \; V_{A}A_{X}}{\rho \left( {I_{P} + {1.6r_{P}}} \right)}\mspace{14mu} {for}\mspace{14mu} I_{M}} > I_{eff}}} & (4)\end{matrix}$

In these equations, γ is a shape factor (equal to a value of 1.5 forglobular spheres and a value of 1.0 for long cylinders aligned parallelto the electric field),^(47,48,63-66) V_(A) (V) is the applied electricpotential difference, p m) is the resistivity of the electrolytesolution, l_(P) (m) is the length of the nanopore, r_(P) (m) is theradius of the nanopore, and l_(M) is the length of the protofibril orfiber. The effective length of the cylindrical nanopore, l_(eff), isdefined by the term (l_(P)+1.6r_(P)) in the denominator of equations (3)and (4), and it accounts for the extension of the electric field linesfrom the nanopore into the bulk solution.⁶⁷

Table 3 lists the mean value of ΔI and the range of ΔI values that wemeasured for each cluster as well as the values for the excluded volumethat we calculated using equation (1) for cluster (i) and the values forthe cross-sectional areas that we calculated using equation (2) forclusters (iii) and (iv). Table 3 also compares the sizes of Aβ₍₁₋₄₀₎aggregates as determined from resistive-pulse analysis with those thatwe determined from analysis of TEM images from the same samples (FIG.10) as well as with those reported in literature. For instance, the meanΔI of the resistive pulses in cluster (i) corresponds to a sphericaldiameter of 5.5 nm (with a range of 5-6 nm), and we measured via TEMthat the smallest spherical aggregates had an average diameter of6.2±1.2 nm (N=18) (FIG. 3A). Similarly, the mean ΔI of the resistivepulses in cluster (iii) due to protofibrils with l_(M)>l_(eff)corresponds to a cylindrical diameter of 4.4 nm (with a range of 3.6 to5.6 nm). In TEM micrographs, we observed protofibrils with an averagediameter of 6.4±1.5 nm (N=117) and with lengths ranging from ˜6 nm to350 nm (FIGS. 10B & 10C); the reported diameter of protofibrils inliterature is ˜5 nm.^(19,21) Finally, the mean ΔI of resistive pulses incluster (iv) due to fibers corresponds to a cross-sectional-area of 36nm² (with a range of 25 nm² to 88 nm²). From the TEM micrographs, weestimated the cross-sectional area of Aβ₍₁₋₄₀₎ fibers to be 51±10 nm²(N=27) based on the two visible widths of the twisting fibers of 5.6±0.8nm and 11.5±1.5 nm (FIG. 10A: Day 3 and FIG. 10D). The literature valuesof the cross-sectional areas of amyloid fibers range from 30 nm² to 90nm^(2.22,23,27). For these three forms of Aβ₍₁₋₄₀₎ aggregates, thegeneral agreement among the sizes determined from resistive-pulseanalysis with those determined by TEM analysis and those reported inliterature demonstrates that resistive-pulse analysis makes it possibleto characterize Aβ oligomers, protofibrils, and fibers. This agreementalso indicates that the cluster analysis produced reasonable assignmentsfor the majority of the resistive pulses. We provide additional evidencefor the accuracy of the cluster analysis in Supporting Information S14.

TABLE 3 Average values of Δ/, excluded volumes Λ, diameters of sphericalAβ₍₁₋₄₀₎ aggregates θ_(s), and cross-sectional areas A_(x) as well thecorresponding cylindrical diameter θ_(c) of rod-shaped Aβ₍₁₋₄₀₎aggregates in each cluster compared to equivalent values measured viaTEM and values reported in literature. <ΔI> Λ θs (min, max) (min, max)(min, max) TEM Values literature value cluster pA nm³ nm nm nm (i):spherical oligomers 324 85 5.5 θc = 6.2 ± 1.2 — (250, 432) (66^(a), 113)(5.0, 6.0) (ii): protofibrils I_(M) ≤ I_(eff) 596 206 — θc = 6.5 ± 2.0θc = 5 ^(Ref. 19,21) (433, 1051) (189, 388) <ΔI> A_(x) θs TEM Valuesliterature value cluster pA nm² nm nm nm (iii): protofibrils I_(M) >I_(eff) 1655 15 4.4 θc = 6.4 ± 1.5 θc = 5 ^(Ref. 19,21) (1087, 2639)(10, 24) (3.6, 5.6) (iv): fibers I_(M) >> I_(eff) 3792 36 6.7 ^(b)W₁ =5.6 ± 0.8 W₁ = 6.6 ^(Ref. 22) (2669, 9552) (25, 88) (5.6, 10.6) W₂ =11.5 ± 1.5 W₂ = 13.2 ^(Ref. 22) Ax = 54 ± 10 nm² Ax = 30-90nm^(2 Ref. 22,23,27) ^(a)Using the average molecular weight density ofAβ₍₁₋₄₀₎ aggregates of 0.81 kDa/nm^(3 Ref. 22,68) and the molecularweight of an Aβ₍₁₋₄₀₎ monomer of 4.3 kDa, the smallest sphericaloligomers detected in cluster (i) contained approximately 12 monomers.^(b)W₁ and W₂ refer to the widths of twisting Aβ₍₁₋₄₀₎ fibers when thefibers are twisted or crossing over themselves, W₁, or when the fibersare lying flat, W₂, on the TEM grid (FIG. 3).²²

In order to estimate the excluded volume, Λ, of the protofibrils withl_(M)<l_(eff) from the resistive pulses in cluster (ii), we made twoassumptions. First, protofibrils pass through the nanopore with theirlong-axis aligned parallel to the electric field resulting in arelatively constant shape factor that can be approximated from the shapefactor of a prolate aligned parallel to an electric field, γ_(∥). Thisalignment is predicted to occur because aggregates approaching thenanopore from the bulk solution experience a strong converging electricfield gradient.^(49,63-65,69-71). Ai and Qian recently modeled thedynamics of nanorods (1 nm×10 nm) approaching a nanopore under verysimilar conditions to those reported here and demonstrated that rodswill completely align with their length axis parallel to the electricfield prior to entering the nanopore.⁷² Furthermore, the distribution oftranslocation times in cluster (ii) was narrower than the distributionin cluster (i) (FIG. 9B), which is consistent with reduced diffusivespreading due to accelerated motion through the pore as a result ofreduced viscous drag on aggregates in cluster (ii) compared to those incluster (i) (see Supporting Information S15 for distributions of t_(d)values in clusters i and ii).^(57,62) Indeed, prolate spheroids movingparallel to their long axis experience less viscous drag than aspherical particle of similar volume.⁷³ These effects combined with thestrong electrophoretic force on an aggregate due to the net negativecharge of an Aβ monomer of −3 at pH 7.0^(15,74) and the high electricfield in the nanopore (V_(A)/l_(eff)=4.5×10⁶ V m⁻¹) likely orientsprotofibril aggregates with their length axis parallel to the electricfield in in the nanopore. The second assumption, based on results byKellermayer et al., was that the elongation of Aβ protofibrils occurs ata constant diameter, 8c, for lengths greater than 6.5 nm.⁸ We confirmedthe validity of this assumption by TEM analysis of the samples used here(see FIG. 10 and Supporting Information S16). Consequently, the excludedvolume of these protofibrils could be described by the equation ofcylinder, A=¼ π θ_(C) ²l_(M), and a system of equations that includesthe shape factor γ_(∥) as a function of the length of the aggregate,l_(M), and ΔI as a function of γ_(∥) and l_(M). We summarized thedetails of these equations, the resulting shape factors, and results ofthis analysis in the Supporting Information S17. Solving this system ofequations while using the values of ΔI from the resistive pulses incluster (ii) and the diameter of protofibrils with l_(M)>l_(eff) fromcluster (iii) (Table 3, θ_(C)=4.4 nm), this analysis returned shapefactors for each translocation event in cluster (ii) that ranged fromγ_(∥)=1.048 to 1.2 (average γ_(∥)=1.13) and excluded volumes that rangedfrom 189 nm³ to 388 nm³ (Table 3).

As a first attempt at examining the peaks in the distribution ofAβ₍₁₋₄₀₎ sizes reported by Cabriolu et al., we generated a histogram ofthe lengths of the protofibrils in clusters (i) and (ii) (FIG. 11) usingthe equations described previously and the Supporting Information S17.The dotted blue lines in FIG. 11 indicate the lengths of protofibrils atwhich Cabriolu et al. observed peaks in the distribution of sizes; theselengths are 6.6, 13.2, and 19.2 nm. Kellermayer et al. reportedsegmented growth of Aβ protofibrils generated by the 25-35 amino acidportion of Aβ₍₁₋₄₀₎ and leading to protofibril lengths of 6.5, 13.3,23.2, 32.5, and 40 nm.^(7,8) These reports together with the observationof several local maxima in FIG. 11 suggest that protofibrils of Aβ₍₁₋₄₀₎are present in solution with certain preferred lengths corresponding tolocal minima in the work for fibril formation.

Since nanopore-based resistive pulse sensing detects single aggregates,the frequency of translocation events is proportional to theconcentration and diffusion constant of the aggregate.^(60,75-77) Forlong protofibrils and fibers, the frequency may also be affected bysteric and entropic effects.^(57,78,79) FIG. 12 shows the frequency oftranslocation events that were assigned to each cluster plotted as afunction of the aggregation time. This analysis provides an indicationof the changes in the concentration of aggregates within each cluster,assuming the diffusion constant and barriers to entering the nanoporeare similar for aggregates within a given cluster. FIG. 12 reveals thatthe frequency of events due to the translocation of large, mature fibersin cluster (iv) increased over time while the frequency of events due tosmall spherical oligomers in cluster (i) decreased as expected fortime-dependent aggregation of Aβ.⁸⁰ FIG. 12 also shows that thefrequency of protofibril translocation in cluster (ii) remainedrelatively constant within the error of the measurement.

In summary, we report the use of nanopores with fluid walls fordetecting and characterizing size distributions of unlabeled aggregatesof Aβ₍₁₋₄₀₎ in situ. These distributions were obtained by measuringhundreds of single aggregates, making it possible to characterize thelarge range of Aβ aggregate sizes and shapes. The results from thisanalysis agree well with those from TEM analysis of the same Aβpreparations and with literature values. Several challenges remain,however, including accurately applying the shape factor, γ, to estimatethe distribution of protofibril lengths in clusters (i) and (ii). Toimprove this analysis it would be helpful to account for possiblerotation of short protofibrils with a low aspect ratio while they movethrough the confining pore as well as the corresponding electric fieldlines around the molecule.⁶⁶

Another challenge involves the time and size resolution of thetechnique; currently, the smallest Aβ aggregates (<dodecamers) could notbe included in the analysis due to resolution limits in ΔI values andt_(d) values. Reducing the translocation speed of Aβ₍₁₋₄₀₎ aggregatesshould improve the determination of ΔI values, reduce the ΔI threshold,and ensure that all t_(d) values can be determined accurately. Inclusionof lipids in the bilayer coating that preferentially interact withaggregated forms of Aβ such as phosphatidylserine or the gangliosideGM1^(81,82) may be one strategy.

Another challenge is that the high ionic strength of the recordingelectrolyte accelerates the aggregation of Aβ (see SupportingInformation S13 and S18). Nanopores with smaller dimensions than thepore used here combined with techniques to increase translocation timesmay ultimately enable the use of electrolyte solutions with physiologicionic strength in these assays.

Despite these challenges, we show that nanopore-based resistive pulserecordings made it possible to characterize the size and shape ofunlabeled aggregates of disease-relevant amyloids in solution. Theparticular strength of nanopore sensing lies in its ability tocharacterize a large number of individual aggregates. This capabilityfor single particle analysis is required to characterize Aβ aggregateswith a wide-ranging, dynamic heterogeneity in size and shape and as wellas to proceed with attempts to correlate cytotoxicity and pathogenicmechanisms with aggregate sizes and shapes.⁶

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Supplemental Information

Table of Contents Section S1. Electrical Resistance ofElectrolyte-Filled 62 Nanopores as a Function of Bilayer Thickness S1.1Model of Electrical Resistance in Electrolyte- 62 Filled Nanopores S1.2Dimensions of Nanopores 63 S1.3 Dimensions of Nanopores after theFormation of 64 a Lipid Bilayer Coating S1.4 Thermal Actuation of theDiameter of Bilayer- 65 Coated Nanopores Section S2. Formation of FluidLipid Bilayers on the 66 Silicon Nitride Substrate and Determination ofLateral Diffusion Constants Section S3. Additional Evidence for aBilayer Coating 68 on the Walls of the Nanopores S3.1 Bilayer CoatingsPrevented Physisorption of 68 Fluorescently-Labeled Streptavidin S3.2Analysis of the Electrical Current Noise Provides 69 Additional Evidencefor the Formation of a Bilayer inside the Pore Section S4. PreciseControl of the Surface Chemistry 70 Section S5. Evidence for the Bindingof Proteins to 71 Lipid-Anchored Ligands in the Bilayer and for theTranslocation of Lipid-Bound Proteins through Bilayer-Coated NanoporesS5.1 Control Experiments with Streptavidin 72 S5.2 Excess Free Biotin inSolution Abolished 72 Resistive Pulses due to Anti-Biotin mAb S5.3Resistive-pulses in the Absence of Biotinylated 73 Lipids could not beTime-Resolved S5.4 Comparison of Diffusion Coefficients of Lipids 75 andDiffusion Coefficients of Proteins in the Nanopore Section S6.Translocations of Non-Spherical Proteins 77 Generate Broad Distributionsof ΔI Section S7. Determining the Most Probable Value 80 of t_(d) andits Error S7.1 Determining the Most Probable t_(d) Value and 80 itsError by Fitting Cumulative Distributions of t_(d) Values S7.2Determining the Most Probable t_(d) Value by 81 Fitting Histograms oft_(d) Values Section S8. Calculating the Charge of Proteins from 82 theTranslocation Time of Lipid-Anchored Proteins S8.1 Derivation ofequation (3) in the main text 82 S8.2 Capillary Electrophoresis forDetermining the 84 Net Charge of Proteins S8.3 Fitting IndividualDistributions of t_(d) with both 87 z and D as Fitting ParametersSection S9. Data Acquisition and Analysis of 88 Resistive Pulses forProtein Detection Section S10. Preparation of Amyloid-Beta Samples 90and Gel-Electrophoresis

Section S1. Electrical Resistance of Electrolyte-Filled Nanopores as aFunction of Bilayer Thickness S1.1 Model of Electrical Resistance inElectrolyte-Filled Nanopores

We explored the simplest possible model for the relationship between theelectrical resistance and the geometry of the nanopore. Based onprevious work, this model assumes that the smallest constriction of ananopore and the resistivity of the electrolyte solution in the nanoporedetermine the total resistance, while the electrical resistance throughthe bulk electrolyte solution from the electrodes to the chip with thenanopore is negligible^(1,2). In the work presented here, thecylindrical nanopore and channel leading to the pore were the narrowestconstrictions (FIG. 13).

We described the nanopore, and the channel leading to the nanopore, ascylinders, each with a radius r (m) and length l(m) that were filledwith an electrolyte with resistivity, ρ (Ω×m). Due to the nanoscalediameter of the pore, the electric field lines converge from the bulksolution to the entrance of the nanopore, resulting in an additionalresistive component called the access resistance, R_(A) ³. Equation (S1)quantifies R_(A) for one entrance to a nanopore³.

$\begin{matrix}{R_{A} = \frac{\rho}{4\; r}} & {S\; 1}\end{matrix}$

Thus, the total resistance is a function of the resistance of thenanopore, R_(P), the access resistance at each side of the pore, R_(AP),the resistance due to the channel, R_(C), and the access resistance fromthe bulk solution below the chip to the channel, R_(AC). We treatedthese resistive components as resistors in series such that equations(S2) and (S3) describe the total resistance between two electrodes onopposite sides of a nanopore:

$\begin{matrix}{{R = {R_{P} + {2\; R_{AP}} + R_{C} + R_{AC}}},{\begin{matrix}\; & \; & \mspace{14mu} &  &  &  & \end{matrix}\begin{matrix}\; & \; \\\; & \;\end{matrix}}} & \left( {S\; 2} \right) \\{{R = {\frac{\rho \; l_{P}}{\pi \; r_{P}^{2}} + \frac{\rho}{2\; r_{P}} + \frac{\rho \; l_{C}}{\pi \; r_{C}^{2}} + \frac{\rho}{4\; r_{C}}}},} & \left( {S\; 3} \right)\end{matrix}$

where l_(P) is the length of the nanopore, r_(P) is the radius of thenanopore, l_(C) is the length of the channel, and r_(C) is the radius ofthe channel (FIG. 13b ).

S1.2 Dimensions of Nanopores

We determined the radius of the nanopores, r_(P), and of the channelsleading to these pores, r_(C), from transmission electron microscopyimages (FIG. 14). To determine the total resistance of a pore for agiven electrolyte, we measured the current through a pore at variousapplied voltages. For these measurements, we used an electrolytesolution containing 500 mM KCl and 10 mM HEPES at pH 7.4 with aresistivity p of 0.1517 Ω×m (measured with a calibrated conductancemeter). Finally, we determined the length of the pore, l_(P), by solvingequation (S3) with the measured value of resistance R, the values ofr_(P) and r_(C) determined from the TEM images, and the known value forthe thickness of the silicon nitride membrane (275±15 nm^(4,5)). FIG. 14shows TEM micrographs of several pores used in this work; the captionlists the dimensions of these pores and specifies for which experimentsthey were used.

For cases in which the cross-section through the nanopore was ellipsoidrather than circular, we calculated an “area-equivalent” radius of thepore, <r_(P), in such a way that the area of a perfect circle withradius r_(P) would be equal to the area of the ellipse with xcorresponding to the major axis and γ corresponding to the minor axis ofthe elliptical cross-section:

<r _(P)>=√{square root over (xy)}.  (S4)

Similarly, we calculated an area-equivalent radius for channels,<r_(C)>, through the silicon nitride with an ellipsoid cross-section by:

<r _(C)>=√{square root over (xy)}.  (S5)

Table 51 lists the dimensions of nanopores used for experiments in themain text and the corresponding experiments.

TABLE S1 Dimensions of all nanopores used for experiments andcorresponding experiment and figure. All dimensions refer to the poresbefore bilayer coating Pore dimensions Figure Description of experimentnm Notes 1c Resistance as a function r_(p) = 14; l_(p) = 12 TEM image inFIG. 14a of bilayer thickness 1d Resistance during a phase r_(p) = 13;l_(p) = 28 — transition of DMPC lipids 2b, 3a, 4a Sensing streptavidin<r_(p)> = 9.6; l_(p) = 18 TEM image in FIG. 14b 3b, 3c, 4b, 4c, Sensinganti-biotin Fab <r_(p)> = 16.5; l_(p) = 22 TEM image in FIG. 14cfragments and anti-biotin monoclonal antibodies (IgG) 5 Sensingstreptavidin as a r_(p) = 10.5; l_(p) = 18 — function of charge and pH 6Sensing aggregated of <r_(p)> = 48; l_(p) = 275 TEM image in FIG. 14damyloid-beta (Aβ) peptidesS1.3 Dimensions of Nanopores after the Formation of a Lipid BilayerCoating

To determine the dimensions of a nanopore after forming a lipid bilayercoating, we used the cylindrical pore shown in FIG. 14a and addedparameters for the thickness of the lipid bilayer, d, and for thethickness of the water layer between the silicon nitride and the lipidbilayer, w_(L), to equation (S3) to obtain equation (S6), which is thesame as equation (1) in the main text:

$\begin{matrix}{R = {\frac{\rho \left( {l_{P} + {2d} + {2w_{L}}} \right)}{{\pi \left( {r_{P} - d - w_{L}} \right)}^{2}} + \frac{\rho}{2\left( {r_{P} - d - w_{L}} \right)} + \frac{\rho \left( {l_{C} + {2d} + {2\; w_{L}}} \right)}{{\pi \left( {r_{C} - d - w_{L}} \right)}^{2}} + {\frac{\rho}{4\left( {r_{C} - d - w_{L}} \right)}.}}} & \left( {S\; 6} \right)\end{matrix}$

Equation (S6) implies that the lipid bilayer and water layer did notconduct ionic current through the nanopore. These two layers, hence,reduced the effective radius of the nanopore by (d+w_(L)) and increasedthe effective length of the pore by 2×(d+w_(L)) (FIG. 13b ).

Note that we measured currents over tens of seconds in order todetermine the resistance of the nanopore, R. As a result, fluctuationsin the water layer or in the thickness of the supported lipid bilayerdue to possible membrane undulations were averaged. We attribute theexcellent agreement between the resistance of the nanopore and thethickness of the lipid bilayers (shown in FIG. 1c of the main text) tothe use of the same chip and lipids with the same chemical head group(phosphatidylcholine) in these experiments. These conditions resulted insimilar interactions between the bilayer, substrate, and water. Inaddition, we used the same cleaning procedure, same methods of preparingliposomes, and same electrolyte in each experiment.

S1.4 Thermal Actuation of the Diameter of Bilayer-Coated Nanopores

To calculate the thickness of a lipid bilayer, and hence, the effectiveopen radius of a nanopore as a consequence of a thermal phase transitionof the lipids, we described the resistivity, ρ, of the electrolyte as afunction of temperature with equation (S7)⁶:

$\begin{matrix}{{\rho = \frac{6\pi \; \eta}{{CN}_{A}{e^{2}\left( {\frac{1}{r_{+}} + \frac{1}{r_{-}}} \right)}}},} & \left( {S\; 7} \right)\end{matrix}$

where the viscosity of water, π (Pa×s), as a function of thetemperature, T (K), is given by⁷:

$\begin{matrix}{{\eta = {\left( {2.414 \times 10^{- 5}{{Pa} \cdot s}} \right) \times 10^{(\frac{247.8K}{T - {140K}})}}},} & \left( {S\; 8} \right)\end{matrix}$

and C (mol×m⁻³) is the concentration of a monovalent salt, N_(A) isAvogadro's constant (mol⁻¹), e (C) is the elementary charge of anelectron, r₊ (m) is the radius of the hydrated cation, and r (m) is theradius of the hydrated anion in the electrolyte. To validate this model,we measured the resistance of a nanopore without a bilayer coating as afunction of temperature. We used an electrolyte containing 500 mM KCland controlled the temperature of the device and electrolyte with aPeltier cooler (Warner Instruments, Hamden Conn.). FIG. 15 shows themeasured resistance as a function of temperature (squares). Note thatthe green curve is not a fit to the data; instead it reflects thecalculated resistance as a function of temperature based on equations(S3), (S7) and (S8). In equation (S8), we used values for r₊ of133×10⁻¹² (m) for K⁺ ions and for r⁻ of 181×10⁻¹² (m) for Cl⁻ ions³.

To change the diameter of the nanopore, we coated the pore with a lipidbilayer of DMPC lipids (both acyl chains of DMPC are saturated andcontain 14 carbons) and varied the temperature while measuring theresistance (Fig. S3, circles). We fit the data in Fig. S3 with equations(S6)-(S8) using the thickness of the bilayer, d, as the only fittingparameter. This fit in the temperature range of 300-310 K returned thered curve (N=5, R²=0.97), and in the temperature range of 280-290 K, itreturned the blue curve (N=5, R²=0.95) (Fig. S3). To calculate thechange in d as a function of the thermal phase transition of the lipidbilayer, we used Maple™ 13 to solve equations (S6)-(S8) for d, with allparameters except temperature held constant (FIG. 2c in the main text).These calculations revealed a change in bilayer thickness, Δd, betweenthe disordered liquid crystalline phase (T>296 K) and the ordered gelphase (T<296 K) of 0.7±0.04 nm (fit in FIG. 2c in the main text). Thisvalue of Δd is similar to reported values for Δd of DMPC bilayers of0.9-1.1 nm^(8,9).

Section S2. Formation of Fluid Lipid Bilayers on the Silicon NitrideSubstrate and Determination of Lateral Diffusion Constants

Reimhult et al. demonstrated that liposome fusion on a silicon nitridesurface forms a single supported lipid bilayer¹⁰. To prepare smallunilamellar vesicles (SUVs), we dissolved the desired lipids in 100 μLchloroform to a lipid concentration of 10 mM. We evaporated the solventunder vacuum using a rotary evaporator to form a lipid film in a roundbottom glass flask with a volume of 10 mL. We resuspended this lipidfilm in an aqueous solution containing 150 mM KCl and 10 mM HEPES at pH7.5 such that the lipid concentration was 2 mM. Finally, we formed SUVsvia tip sonication (Branson Sonifier 150) of the solution with a powerof 3-4 W for ˜10 min and stored these solutions at 4° C. for up to 4days. We formed the supported lipid bilayer on the chips as described inthe Methods Section of the main text.

We used epifluorescence microscopy to confirm the formation of a fluidlipid bilayer for experiments with bilayer-coated nanopores. Tovisualize the lipid bilayer, we prepared all liposomes with 0.8 mol % oflipids labeled with the fluorophore rhodamine B(1,2-dipalmitoyl-sn-glycero-3-phosphoethanolamine-N-(lissamine rhodamineB sulfonyl)) (Rh-PE, Avanti Polar Lipids). To form the lipid bilayer, weincubated the top side of the chip in a solution containing Rh-PElabeled liposomes for 5-10 min followed by rinsing with pure water for5-10 min. We used a Nikon E600FN upright microscope equipped with anEvolution MP (Media Cybernetics, Canada) camera and a 60× water-dippingobjective (NA=1.00) to image the bilayers. FIG. 16a shows a fluorescentmicrograph (false-colored in red) that confirmed the presence of asupported lipid bilayer on the silicon nitride substrate. The sharplydefined square in the middle of the image is the free-standing siliconnitride membrane. A line scan across the silicon nitride membrane (solidwhite line) quantified the fluorescence intensity as a function of theposition along this line (FIG. 16a ). Interestingly, we observed fourvalues of fluorescence intensity along this path. The lowest intensityoccurred in area 1 (I=528±15); a location in which the bulk silicon chipsupported the silicon nitride membrane. Moving along the line scan to anarea over part of the free-standing silicon nitride membrane, indicatedas area 2, we observed a slightly greater intensity (I=873±31) than inarea 1. We attribute the reduced intensity in area 1 compared to area 2to destructive interference from light reflected by the bulk siliconchip below area 1¹¹. Moving further along the line scan toward thecenter of the free-standing, silicon nitride membrane (area 3), weobserved a fluorescence intensity approximately twice the intensity(I=1,542±29) of area 2. This result indicates that area 3 containedapproximately twice the amount of fluorescent Rh-PE lipids than area 2and is consistent with a supported bilayer on both sides of thefree-standing, silicon nitride membrane. Finally, area 4, in the centerof the free-standing, silicon nitride membrane and at the location ofthe nanopore, had the greatest fluorescence intensity (I=2,222).

We attribute this high intensity to the presence of a lipid bilayer onthe vertical walls of the nanopore and channel (see Fig. S1), and hence,to an increased number of Rh-PE lipids in the optical path. Fig. S4 eshows three additional fluorescence micrographs with a spot of highintensity in the center of the free standing, silicon nitride membraneat the precise location of the nanopores. The width of these spots at1/e² of their maximum intensity, w_((1/e) ₂ ₎ ranged from 0.8 μm to 1.8μm. These values are 2-5 times larger than the theoreticaldiffraction-limited spot size of 0.33 μm that we calculated for thisobjective with equation (9)¹²:

$\begin{matrix}{{w_{({1/e^{2}})} = \frac{2\; \lambda}{n\; \pi \; {NA}}},} & (9)\end{matrix}$

where, λ, is the wavelength of light (here ˜700 nm), n is the index ofrefraction of the medium (here 1.33), and NA is the numerical apertureof the objective (here 1.00). The larger than expected values for thesize of the diffraction-limited spot could be due to reflection orrefraction occurring at the interface between the aqueous solution andthe transparent silicon nitride structure of the nanopore.

Furthermore, equation (9) predicts the size of the smallest spot thatcan be obtained theoretically given all of the optics were perfect—realmicroscopes typically cannot reach this theoretical limit. Regardless ofdeviations from the theoretically expected spot size, the images in FIG.16e confirm the observations in FIG. 16a, b with regard to thefluorescence intensity from bilayers on the chips. These results, incombination with the well-defined shrinkage of the pore diameter bybilayer coatings of various lipids (FIG. 1c ) and the results from FIGS.3 and 4, suggest that a supported lipid bilayer formed on the siliconnitride, on the inner walls of the nanopore and channel, and on theunderside of the free-standing, silicon nitride membrane.

To confirm the fluidity of the supported lipid bilayers and to determinelateral diffusion constants of the lipids, we preformed fluorescencerecovery after photobleaching (FRAP) experiments (FIGS. 16a and b ) onthe bilayer at a location outside, but near, the free-standing, siliconnitride membrane (i.e., in area 1 of FIG. 16a )¹³. We analyzed theseimages by calculating the difference between the mean fluorescenceintensity of the photobleached spot and a second spot on the samebilayer that was not photobleached. We normalized to the maximumdifference between these two intensities and determined the diffusioncoefficients by the equation, D_(L) (nm²×μs⁻¹)=0.224×ω² (nm)²/t_(1/2)(μs), where ω is the radius of the bleached spot and t_(1/2) is the halftime of the fluorescence recoveryl^(4,15). We obtained the value oft_(1/2) from an exponential curve fit through the data (FIG. 17b ). Onthe chip used in FIG. 17 and shown in FIG. 14b , the diffusioncoefficient for bilayers containing POPC lipids was 1.13±0.13 nm²×μs⁻¹and for bilayers containing DΔPPC lipids it was 1.56±0.16 nm²×μs⁻¹.These values are close to reported values of diffusion coefficients ofsupported bilayers, which range from 2 nm²×μs⁻¹ to 5 nm²×μs⁻¹ and aretypically obtained on glass or SiO₂ surfaces instead of Si₃N₄surfaces^(16,17).

Section S3. Additional Evidence for a Bilayer Coating on the Walls ofthe Nanopores S3.1 Bilayer Coatings Prevented Physisorption ofFluorescently-Labeled Streptavidin

To provide additional evidence that a supported lipid bilayer formed onthe walls inside the nanopores, we incubated a chip containing ananopore with rhodamine-labeled streptavidin (SA-TRITC). We incubatedthe same piranha-cleaned chip with SA-TRITC in one experiment afterforming a supported lipid bilayer on the chip (and in the pore) and inthe other experiment before forming the bilayer. FIG. 18a shows that inthe absence of a bilayer coating, SA-TRITC physisorbed to the siliconnitride surface including in the center of the silicon nitride windowwhere a bright spot of fluorescence indicates that SA-TRITC alsophysisorbed onto the walls inside the uncoated nanopore. Similar to theline scans shown in FIG. 16, the width of the diffusion limited highintensity spot in FIG. 18a was 0.9 μm. In contrast, FIG. 18b shows thatthe same chip, after being cleaned and subsequently coated with a lipidbilayer, did not physisorb a detectable amount of rhodamine-labeledstreptavidin. Additionally, at the center of the silicon nitride windowand the location of the nanopore, we did not detect an increase in theintensity of fluorescence. This result suggests that the vertical wallsinside the nanopore were also coated with a lipid bilayer that preventedthe physisorption of SA-TRITC.

S3.2 Analysis of the Electrical Current Noise Provides AdditionalEvidence for the Formation of a Bilayer Inside the Pore

Since supported lipid bilayers are fluid sheets, lipid molecules withinthe bilayer are in dynamic motion. In addition, the water layer betweenthe lipid bilayer and the silicon nitride substrate fluctuates around anaverage value. We hypothesized that the resulting bilayer undulationsmay influence the electrical noise in current recordings. FIG. 19, bcompare the power spectra of the noise as a function of frequency fortwo chips with nanopores before and after generating a supported lipidbilayer. As expected, when the pore was coated with a fluid lipidbilayer, the noise increased at low frequencies (<2 kHz) compared to theuncoated pore. Since this increased noise was likely due to dynamicmotions consistent with a supported lipid bilayer inside the nanopores,it provides additional evidence for the formation of a lipid bilayer onthe walls inside the nanopores. To test this hypothesis, we obtainedpower spectra of the noise with a chip that contained a very smallnanopore with area-equivalent diameter of 9 nm. The diameter of thisnanopore was too small for a supported lipid bilayer to form on theinterior walls of the pore. In this case, spreading offluorescently-labeled liposomes on the top side of the chip coated onlythis top side while no increased fluorescence could be detected at thelocation of the pore and no doubled fluorescence intensity could bedetected from creeping of fluorescent bilayers through the pore to theother side of the silicon nitride window. FIG. 19, d shows that in thiscase, the electrical noise in the system remained relatively unchangedcompared to the nanopores with a diameter large enough to accommodate abilayer coating inside the pore. In both experiments, we confirmed byFRAP experiments that the bilayer near the pore was fluid. Togetherthese results provide additional evidence for the formation of a fluidlipid bilayer on the walls inside the nanopore.

Section S4. Precise Control of the Surface Chemistry

The surface chemistry of bilayer-coated nanopores can be preciselycontrolled by the nature of the polar head groups of the lipids used inthe bilayer coating. To demonstrate this capability, we formed severalliposome preparations from POPC lipids that contained different molefractions of 1,2-dioleoyl-sn-glycero-3-phosphate (DOPA), a lipid with anegatively charged head group. After vesicle fusion of these liposomesonto S1/S13N4 chips with a nanopore to generate the bilayer coating, wemeasured the electrical resistance through the nanopore. Since underconditions of low ionic strength, positively charged ions accumulatenear the surface of a negatively charged bilayer, we expected to observea decrease in the resistance of the pore with increasing mole fractionsof DOPA.¹⁸ FIG. 20 confirms that the resistance of the bilayer coatednanopore decreased with increasing mole fractions of DOPA lipids insidethe nanopore walls.

To demonstrate that this decrease in the resistance was a nanoscopiceffect, as predicted by the Gouy-Chapman theory, we compared theresistance of a conical pore (tip diameter 500 nm) whose walls werecoated by an electrically neutral bilayer (˜99 mol % POPC) to theresistance of the same pore with a negatively charged bilayer coating(˜40 mol % DOPA and ˜59 mol % POPC). Using the same electrolyte as inFIG. 20, the resistance of this large pore remained independent of thepresence of a neutral or negatively charged bilayer coating (FIG. 21).This result confirms that the observations in FIG. 20 were due tonanoscopic phenomena in pores with diameters that are significantlysmaller than 500 nm; it also provides additional evidence for theformation of a negatively charged bilayer on the walls inside thenanopore.

Section S5. Evidence for the Binding of Proteins to Lipid-AnchoredLigands in the Bilayer and for the Translocation of Lipid-Bound ProteinsThrough Bilayer-Coated Nanopores

We used the amplitude of resistive pulses, ΔI, to distinguish thetranslocation of streptavidin (SA), monoclonal anti-biotin antibody(mAb), and anti-biotin Fab fragments (Fab) through nanopores. Thesepores were coated with a bilayer that contained biotinylated lipids(biotin-PE) at the specified mole fractions. To confirm that resistivepulses were due to proteins that were bound to biotin-PE, we performedseveral control experiments that entailed: 1) replacing the electrolytein the top compartment with a solution that did not contain SA toinvestigate if the frequency of events would be reduced (as expected forunbound SA) or remain the same (as expected for lipid-anchored SA); 2)presenting an excess of soluble biotin in solution in the presence ofmAb on a chip that contained a bilayer-coated nanopore with biotin-PElipids; and 3) detecting the translocation of SA, mAb, and Fab withbilayer-coated nanopores that did not contain biotin-PE lipids. Wedescribe these experiments in detail in the following paragraphs, butbriefly, when the protein could bind to biotin-PE in the bilayercoating, we observed 20-500 times more frequent translocation eventsthan under conditions in which the protein could not bind to biotin-PE.Furthermore, we observed significantly prolonged translocation timeswhen proteins could bind to biotin-PE; these increased t_(d) valuespermitted time-resolved measurements of ΔI (and therefore quantitativeestimation of protein volume). Finally, the viscosity of the bilayercoating influenced the translocation time of proteins passing throughthe nanopore only when proteins could bind to biotin-PE. We show thatthe diffusion coefficients of the proteins in the nanopore under theseconditions were similar to the diffusion coefficients of the lipids inthe bilayer coating, and we present a simple model for predicting thetranslocation times for proteins through a nanopore. We conclude fromthese results that bilayer-coated nanopores with biotin-PE lipidsdetected specifically proteins that bound to these lipid anchored biotingroups. Moreover, resistive pulses were due to the translocation ofprotein-(biotin-PE) complexes through the nanopore because biotin-PEremained mobile within the fluid bilayer coating of the nanopore. Theunique ability of bilayer-coated nanopores to exploit the viscosity of afluid bilayer coating in order to reduce the translocation speed ofproteins made it possible to determine the volume of proteins accuratelyand, consequently, to distinguish anti-biotin Fab fragments fromanti-biotin mAbs.

S5.1 Control Experiments with Streptavidin

We hypothesized that SA would remain bound to biotin-PE for extendedperiods of time due to the very slow off-rate of the SA to biotininteraction (k_(off)˜10⁻⁶ s⁻¹)¹⁹. Consequently, after washing the liquidcompartments to remove unbound SA from solution, we expected to observea continuation of frequent resistive pulses with a nanopore coated witha bilayer containing biotin-PE. To start this experiment, we generated abilayer-coated nanopore that contained 0.15 mol % biotin-PE lipids.After adding 6 pM SA to the electrolyte on top of the fluidic setup, weapplied a voltage of −0.1 V and observed resistive pulses at a frequencyof ˜45 s⁻¹ (FIG. 22a ). Consistent with resistive pulses due to proteinswith a net negative charge, we observed a 28-fold decrease in thefrequency of resistive pulses after changing the polarity of the appliedvoltage to +0.1 V (frequency of ˜1.6 s⁻¹). After rinsing the fluidicchannels periodically for 3 h, we again applied a voltage of −0.1 V andobserved resistive pulses at a frequency similar to the frequency beforewashing (41 s⁻¹ versus 45 s⁻¹, FIG. 22a ). When we repeated thisexperiment with a bilayer-coated nanopore that did not contain biotin-PElipids, we observed almost no resistive pulses (frequency of ˜0.09 s⁻¹,FIG. 2b and FIG. 22a ). Together these results confirm that the observedresistive pulses were due to translocation of SA bound to lipid-anchoredbiotin through the nanopore while biotin-PE remained mobile within thefluid bilayer coating.

S5.2 Excess Free Biotin in Solution Abolished Resistive Pulses Due toAnti-Biotin Ab

To provide additional evidence for the specificity of detection ofproteins that were targeted by lipid-anchored biotin (i.e. streptavidin,anti-biotin mAb, or anti-biotin Fab fragments) with bilayer-coatednanopores, we performed a control experiment by adding a highconcentration of soluble biotin (10 μM) to an ongoing experiment with abilayer-coated nanopore that contained biotin-PE. We hypothesized thatthe excess biotin in solution would compete for biotin binding sites onthese proteins, and consequently, the frequency of resistive pulsesafter the addition of biotin would decrease. To start this experiment,we coated a nanopore with a bilayer that contained biotin-PE lipids.After adding 20 nM anti-biotin mAb to the solution in the top fluidcompartment, we observed resistive pulses at a frequency of 34 s⁻¹(FIGS. 22b and 23a ). After adding 10 μM soluble biotin to the solution,we observed significantly fewer resistive pulses (frequency of 1.3 s⁻¹)demonstrating that approximately 96% of the resistive pulses in Fig. S11a were due to mAb that was bound to biotin-PE (FIG. 22b and FIG. 23b ).This result indicates that the detection of the proteins (i.e.streptavidin, mAb, or Fab) required binding of the proteins to biotin-PElipids and that the proteins moved through the nanopore while bound tomobile biotin-PE lipids in the fluid, lipid bilayer coating.

We hypothesized that in this control experiment, the excess biotin insolution would occupy the majority of the binding sites of anti-biotinmAb and would therefore prevent the mAb from binding to biotin-PElipids. Consequently, we expected the translocation of mAb through thenanopore to occur faster than before the addition of excess biotin (i.e.when the mAb moved through the nanopore as a lipid-anchoredmAb-biotin-PE complex). The histograms of t_(d) and ΔI values in FIGS.23a and 23b confirmed this expectation by illustrating that the mostfrequently observed translocation time decreased from 54±8 μs to ˜27 μsafter adding excess biotin in solution. This result indicates that theviscosity of the bilayer coating reduced the translocation speed (i.e.increased the value of t_(d)) of mAbs that were bound to biotin-PElipids in the bilayer by at least a factor of two compared totranslocation of unbound mAbs. Furthermore, in contrast to thetranslocation times for mAb that was bound to biotin-PE (t_(d)=54±8 μs),translocation times for unbound mAb (t_(d) 27 μs) were shorter than thebandwidth of the recording setup (Supplementary Section S9), andconsequently, the values for ΔI were attenuated because they were nottime resolved (FIG. 23b ).

S5.3 Resistive-Pulses in the Absence of Biotinylated Lipids could not beTime-Resolved

To confirm that time-resolved detection of streptavidin, anti-biotinmAb, and anti-biotin Fab fragments with bilayer-coated nanoporesrequired biotin-PE lipids in the bilayer coating, we generatedbilayer-coated nanopores that did not contain biotin-PE and added SA,mAb, or Fab fragments. We analyzed the current recordings to determinethe frequency of resistive pulses, the values of t_(d), and themagnitudes of ΔI. FIG. 22 shows that bilayers without biotin-PE resultedin resistive pulses at 20-500-fold lower frequencies than bilayers withbiotin-PE (see also FIGS. 23 and 24 a for original current traces).These results suggest that biotin-PE in the supported lipid bilayerconcentrated the proteins from solution onto the surface of the fluidbilayer via protein-ligand binding and that these surface bound proteinstranslocated through the pores at a higher frequency than proteins fromthe bulk electrolyte. Furthermore, it suggests that the resistive pulseswe observed with bilayer-coated nanopores containing biotin-PE weremostly (>90%) due to the movement of protein-biotin-PE complexes withinthe bilayer coating of the nanopore.

In the absence of biotin-PE in the bilayer coating, we expected thetranslocation of proteins through the pore to occur faster than in poresthat were coated with a bilayer containing biotin-PE since in the lattercase the viscosity of the bilayer can reduce the translocation speed ofproteins bound to lipids. As a result, we expected to observe reducedvalues of t_(d) and attenuated values of ΔI compared when biotin-PE wasnot used in the bilayer coating. Due to the non-Gaussian distributionsof t_(d), we compared the values of translocation times, t_(d), that weobserved most frequently in each distribution of t_(d) values (i.e. themost probable value). For instance, the translocation of anti-biotin mAbthrough a bilayer-coated pore without biotin-PE lipids was significantlyfaster (t_(d) 22 μs) than the translocation through the same pore with abilayer coating that contained biotin-PE (t_(d)=54±8 μs) (FIG. 23). Thetranslocation time of 22 μs was below the lower limit of accuratequantification of t_(d), and consequently, we obtained reduced values ofΔI when the bilayer coating did not contain biotin-PE (Fig. S11 c).Thus, we did not resolve a complete distribution of ΔI, and we observedfew values of ΔI (<10%) larger than 500 pA (FIG. 23c ).

We obtained similar results from analyzing resistive pulses due to thetranslocation of Fab fragments; the translocation of Fab fragmentsthrough a bilayer-coated pore without biotin-PE lipids was faster (t_(d)20 μs, FIG. 24b ) than the translocation through the same pore with abilayer coating that contained biotin-PE (t_(d)=78±5 μs, FIG. 24c ).Again, we observed reduced values of ΔI and an incomplete distributionof ΔI (FIG. 24b ) when the bilayer did not contain biotin-PE lipids. Incontrast, when the bilayer coating contained biotin-PE, the increasedtranslocation time of Fab through the nanopore resulted in a fullyresolved distribution of ΔI with an average value of 254±39 pA (FIG. 24c). Using equation (2) from the main text, we estimated a volume of172±31 nm³ for the Fab fragments; the expected volume from literature is˜140 nm³ ²⁰. Together, these results provide evidence that the localviscosity of the bilayer coating in combination with lipids presentingligands provides an effective novel strategy for increasing thetranslocation time of specific proteins that are bound to lipid-anchoredligands.

To further increase the translocation time of Fab fragments, wegenerated a bilayer coated nanopore that contained biotin-PE andcholesterol. The presence of cholesterol in a lipid bilayer can increaseits viscosity significantly¹³. We hypothesized that the translocation ofFab through this bilayer-coated nanopore would be slower than with abilayer coating of purely POPC and biotin-PE. For these experiments, weformed the bilayer coating from liposomes prepared with 0.15 mol %biotin-PE, 0.8 mol % Rh-PE, 49.5 mol % POPC, and 49.5 mol % cholesterol.As expected, in the presence of anti-biotin Fab fragments, we observedtranslocation times (t_(d)=175±4 μs, FIG. 24d ) approximately twice aslong as with bilayers that did not contain cholesterol (t_(d)=78±5 μs,FIG. 24c ). We obtained a value of ΔI of 275±29 pA, which corresponds toa volume of 178±19 nm³ (Fig. S12 d). Given that the reported volume ofFab fragments are ˜140 nm³, these results suggest, once again, that abilayer coating with increased viscosity made it possible to resolvetranslocation events of individual proteins completely in time and thatthis capability makes it possible to determine the volume of Fabfragments accurately.

S5.4 Comparison of Diffusion Coefficients of Lipids and DiffusionCoefficients of Proteins in the Nanopore.

We expected the diffusion coefficient of the lipids in the bilayer,D_(L), and the diffusion coefficient of the proteins in the nanopore,D_(P), to have similar values since diffusion coefficients oflipid-anchored proteins are determined by the diffusion coefficients oftheir lipid anchor in a lipid bilayer²¹⁻²³. Table 2 in main textcompares D_(L) to D_(P) using equation 3 from the main text to calculateD_(P) based on measured t_(d) values. For this comparison, we used themost probable value of t_(d) and the known charge of the protein tocalculate the diffusion coefficient, D_(P). Recent work by Talaga and Lienables an additional method for determination of D_(P) by fittingindividual distributions of t_(d) values to a biased diffusion firstpassage time model developed by these authors²⁴. Here, we comparediffusion coefficients obtained by these fits to the entire distributionof t_(d) values with diffusion coefficients of the lipids, D_(L),determined by FRAP.

The model developed by Talaga and Li is shown in equation (S10); thisfunction describes the distribution of values of t_(d) that result fromthe translocation of charged proteins through a nanopore in the presenceof an electric field²⁴:

$\begin{matrix}{{P\left( t_{d} \right)} = {\frac{\left( {{vt}_{d} + l_{P}} \right) \times e^{\frac{- {({l_{P} - {vt}_{d}})}^{2}}{4{Dt}_{d}}}}{t_{d} \times \sqrt{4\; {Dt}_{d}\pi}}.}} & \left( {S\; 10} \right)\end{matrix}$

Here, ν (m×s⁻¹) is the electrophoretic drift velocity and D (m²×s⁻¹) isthe diffusion coefficient of the protein within the nanopore. Briefly,this equation assumes that a particle (or protein) moves in onedimension with an electrophoretic mobility u_(e) (m²×V⁻¹×s⁻¹) and thatits motion is driven by a linear electric field, s (V×m⁻¹), whichresults in the electrophoretic drift velocity, ν=ε×u_(e). It alsoassumes that the protein moves from a starting point (signified in timeby the beginning of the resistive pulse) to an infinite sink that is adistance l_(p) away (signified in time by the end of the resistivepulse). Further details on the derivation can be found in the article byTalaga and Li²⁴⁻²⁶.

Since the values of t_(d) result from the translocation of a protein, abest-fit analysis of the distribution of t_(d) values from proteintranslocation experiments with equation (S10) provides the diffusioncoefficient of the proteins in the nanopore (i.e. D=D_(P)). As shown inTable S2, the values of D_(P) were similar to values of D_(L) when thebilayer coating contained biotin-PE lipids and when the proteins wereable to bind to the lipid-anchored biotin moiety. Typically we observedvalues of D_(P) that were within ±31% of the value for D_(L), with amaximum deviation of +117%. When the bilayer coating did not containbiotin-PE or when the protein did not bind to the lipid-anchored biotinmoiety (i.e., in the presence of excess biotin free in solution), thisanalysis determined values of D_(P) that were at least 3-fold greaterthan the value of D_(L). Although these D_(P) values were onlysemi-quantitative due to the incomplete distribution of such short t_(d)values, they indicate that the diffusion coefficient of unbound proteinsthrough the nanopore did not depend on the viscosity of the bilayercoating. Moreover, the agreement between D_(P) of proteins bound to alipid-anchored ligand and D_(L) supports the hypothesis that thefluidity of the bilayer coating determined the translocation time oflipid-anchored proteins through the nanopores. These results providefurther evidence for the formation of a fluid, bilayer coating withinthe nanopore.

TABLE S2 Comparison of diffusion coefficients of lipid-anchored proteinswithin the nanopore, D_(P), determined by equation (S10) with diffusioncoefficients of lipids in the bilayer coating, D_(L). D_(L) ^(a) D_(P)^(b) Δ_(D) ^(c) Protein Lipid Bilayer (nm² μs⁻¹) (nm² μs⁻¹) % SA^(d)POPC + biotin-PE 1.13 ± 0.13 1.4 ± 0.1 +24 SA^(d) DΔPPC + biotin-PE 1.56± 0.16 1.7 ± 0.1 +9 mAb^(e) POPC + biotin-PE 1.29 ± 0.13 2.8 ± 0.2 +117Fab^(e) POPC + biotin-PE 1.27 ± 0.13 1.7 ± 0.1 +31 Fab^(e) 50 mol % POPCand 0.31 ± 0.03  0.6 ± 0.05 +100 50 mol % cholesterol + biotin-PE^(a)D_(L) was calculated based from the FRAP method as described inSupplementary Section S2. ^(b)Diffusion coefficient of the protein,D_(P), in the nanopore as obtained from the best-fit of the cumulativedistributions of t_(d) values (see section S7.1) to equation (S13),which is the integrated form of equation (S10). ^(c)Delta (Δ_(D)) wascalculated by: 100 × (D_(P) − D_(L))/D_(L) ^(d)Experiments wereperformed with the nanopore shown in Supplementary FIG. S2b.^(e)Experiments were performed with the nanopore shown in SupplementaryFIG. S2c.

Section S6. Translocations of Non-Spherical Proteins Generate BroadDistributions of ΔI

FIG. 4 in the main text shows that the distributions of ΔI values forstreptavidin and Fab fragments were significantly narrower than thedistribution for the IgG antibodies. On first sight, the two maxima inFIG. 4c might be attributed to a contamination by other proteins in thesolution of anti-biotin IgG antibodies. Closer inspection of the datareveals, however, that these contaminants would have to bindspecifically to biotin, since neither of the two peaks in FIG. 4c werepresent in control experiments with pores that were coated with the samebilayer but without biotinylated lipids (FIG. 23). The broaddistribution in FIG. 4c was, however, not caused by a contamination ofanti-biotin Fab fragments in the solution of anti-biotin IgG antibodiesbecause Fab fragments would result in a narrow peak in the distributionwith a most frequently observed ΔI value ˜0.25 nA (FIG. 4b ), while thetwo maxima in FIG. 4c were located at ΔI values of ˜0.4 nA and ˜1.0 nA.Therefore, we attribute the broad distribution of ΔI values in FIG. 4bprimarily to the complex molecular shape of IgG antibodies (γ≠1.5)compared to the approximately spherical shape (γ≈1.5) of streptavidinand Fab fragments. In order to provide an estimate for the shape factorof IgG antibodies, we considered their thickness of 2.4 nm and volume of347 nm³ ²⁷ and approximated their shape by an oblate spheroid (i.e., bya lentil-shaped particle) with a volume equal to IgG antibodies and apole-to-pole diameter, A, equal to the thickness of IgG antibodies(A=2.4 nm). This approximation yields an oblate spheroid with anequatorial diameter, B, of 16.6 nm. The shape factor, γ, of an oblatespheroid with diameters A and B depends on the orientation in which ittranslocates through the pore². FIG. 25 illustrates this orientationdependence of γ graphically. For the two extremes of translocation withthe pole-to-pole axis of the spheroid oriented perpendicular to thelength axis of the pore, Grover et al predicted γ=1.1 and fortranslocation with the equatorial axis oriented perpendicular to thelength axis of the pore, they predicted γ≈5.0². The two dashed red linesin FIG. 4c in the main text indicate ΔI values for these two values of γas predicted theoretically by equation (2) in the main text for oblatespheroids with diameters A and B and a volume of 347 nm³. Since thesetwo values of ΔI represent the extremes with regard to the orientationduring translocation, the majority of the experimentally observed valuesof ΔI would be expected to lie between these extremes. FIG. 4c confirmsthis expectation and provides the first experimental support thatresistive pulse analysis may yield information about the shape (based onthe distribution of ΔI values) and orientation (based on the individualΔI value) of proteins with known volumes during their translocation, aspredicted theoretically by Grover et al in 1969². Previously, Mathe etal. observed orientation dependent translocation in nanopore-based DNAexperiments through α-hemolysin pores' and Akeson et al. observed largevariations in ΔI for the same population of nucleic acids due to variousphysical processes²⁹.

As mentioned before, the two orientations in FIG. 25 represent the twoextremes, realistically a lipid-anchored protein will probably not movethrough the pore in only one orientation but in many orientations as itrotates around its lipid anchor. To examine the possibility of rotation,we estimated the time it would take an antibody to rotate 2π radians(360°) around one axis based on equations (S11) and (S12)³¹:

<θ²>=2D _(r) t,  (11)

where θ (rad) is the degrees of rotation, D_(r) (rad² s⁻¹) is therotational diffusion coefficient and, t is (s) the time. Using theeffective radius of an IgG antibody determined from diffusioncoefficient measurements³² (R_(eff)=5.5 nm), we estimated D_(r) for anIgG antibody from equation S12³¹:

$\begin{matrix}{{D_{r} = {\frac{k_{B}T}{f_{r}} = \frac{k_{B}T}{8\; \pi \; \eta \; R^{3}}}},} & (12)\end{matrix}$

where k_(B) (J K⁻¹) is the Boltzmann constant, T (K) is the temperature,and f_(r) is the rotational friction coefficient. Based on thesecalculations, which were derived for spherical particles, we estimatedthat the average time for an antibody to complete one rotation would be˜18 μs. We also calculated the time for one rotation of a disk with asimilar size to an IgG antibody and obtained a value of ˜26 μs³¹. Thesetimes are approximately one third of the translocation time of theantibody through the nanopore (FIG. 3c in the main text). Consequently,the rotation of the antibody while inside the nanopore may result in avalue of γ that is the average of the two extreme values, which wouldyield <γ>=3.1. This hypothesis is consistent with the peak at ΔI˜1.0 nAin the distribution of ΔI values for the mAb as indicated by the reddashed line in FIG. 4c of the main text. The additional peak in FIG. 4cat ΔI˜0.4 nA might be due to factors that are not considered inequations (S11) and (S12). For instance, the rotational diffusioncoefficient predicted by equation (S12) assumes a spherical protein thatis free in solution. Here, the protein was not spherical and attached toa surface inside the confined volume of a nanopore. All three effectslikely increase the average time it takes for the antibody to complete afull rotation. This increased time in combination with steric effectsinside the confined volume of the nanopore may result in a preferredorientation of the antibody in the nanopore (i.e. FIG. 25a ) that ismaintained throughout most of the translocation time. Anotherpossibility is the alignment of the antibody within the electric fielddue to a dipole moment within the molecule. Due to the shape of the IgGantibody, such an alignment would be most likely along its length axisand result in the orientation of the mAb shown in FIG. 25a and a peak inthe ΔI distributions at a value of γ of approximately 1.1. In addition,hydrodynamic effects as a result of rotation may drive antibodiestowards the wall of the pore, which would also favor the orientationshown in FIG. 25 a.

To provide a second example of a broad distribution of ΔI obtained witha non-spherical protein, we employed a bilayer coated nanoporecontaining biotin-PE lipids in the bilayer coating, streptavidin, and abiotinylated IgG antibody (anti-catalase antibody, AbCam®). In thisexperiment, streptavidin bound to the biotin-PE lipids and translocatedthrough the pore resulting in resistive pulses with small values of ΔI(FIG. 26a ). Subsequent addition of the biotinylated-IgG antibody andthe translocation of the lipid-anchored, streptavidin-IgG complexreturned large values of ΔI and an even broader distribution of valuesfor ΔI (FIG. 26b ) than those from the translocation of the anti-biotinmAb (FIG. 23a and FIG. 4c from the main text). We expected this resultsince the shape of the streptavidin-IgG complex deviates even furtherfrom a spherical shape than an IgG antibody. We approximated thestreptavidin-IgG complex as an oblate spheroid with a pole-to-polediameter of 2.4 nm and an equatorial diameter of 18.8 nm; the shapefactor of such an oblate spheroid would be γ=1.1 when the pole-to-poleaxis is oriented perpendicular to the length axis of the pore and γ=5.5when the equatorial axis is oriented perpendicular to the length axis ofthe pore. FIG. 26b shows that approximately 95% of the values for ΔIwere between the expected ΔI for the protein complex given the molecularvolume of the complex and these values for γ.

Section S7. Determining the Most Probable Value of t_(d) and its Error

S7.1 Determining the Most Probable t_(d) Value and its Error by FittingCumulative Distributions of t_(d) Values

In the main text, we report the most frequently observed value of t_(d),located at the absolute maximum of each distribution of measured t_(d)values. We quantified these most probable values of t_(d) by generatingcumulative distributions of measured t_(d) values. To generatecumulative distributions we summed the relative number of observationsthat occurred at or below a specified t_(d) value (x-axis), therebyeffectively integrating the data³³. Cumulative distributions areadvantageous compared to the histograms shown in FIG. 3 in the main textbecause they are generated from all t_(d) values without binning thedata³³. To fit these cumulative distributions we integrated equation(S10) to obtain equation (S13) and fit the cumulative t_(d) data to thisequation:

$\begin{matrix}{{A\left( t_{d} \right)} = {\frac{1}{2}{{erfc}\left\lbrack \frac{\left( {l_{p} - {vt}_{d}} \right)}{2\sqrt{{Dt}_{d}}} \right\rbrack}}} & ({S13})\end{matrix}$

To determine the most probable t_(d) value for a given distribution, weset the second derivative of the fitted equation (S13) equal to 0 andsolved for t_(d). The most probable t_(d) values determined from thecumulative distributions shown in FIG. 27 are plotted in FIG. 28 inSection S8.1. To report an error for each most probable t_(d) value, wevaried the fitting parameters, including the length of the nanopore(l_(P)) and the diffusion coefficient (D_(L)), by their measured errorand reported the maximum deviation in t_(d). The maximum error in l_(P),as estimated from the data in FIG. 1C in main text, was ±1 nm while themaximum error of diffusion coefficients of lipids in supported lipidbilayers as determined by FRAP was ±10%¹³. This method resulted in mostprobable t_(d) values with errors that ranged from ±2% to ±23% of themost probable value of t_(d).

FIG. 27 shows that cumulative distributions whose most probable t_(d)values differed by only 3 μs could be resolved (see the black and reddata) if the experiment was performed on the same chip, with the samebilayer, and under the same experimental conditions. This highresolution is likely to result from errors in l_(P) that are expected tohave nearly the same systematic error for all recordings and wouldtherefore be expected to be significantly smaller than ±1 nm. The errorsof up to ±23% of the most probable t_(d) values reported above refer toseparate experiments, possibly with different chips, when the chips werecleaned and fresh bilayers were formed between each experiment.

S7.2 Determining the Most Probable t_(d) Value by Fitting Histograms oft_(d) Values

In the experiments for determining the most probable values of t_(d) forthe translocation of streptavidin at different pH values of theelectrolyte (FIG. 5 in the main text), we found that a few of thecumulative t_(d) distributions could not be fit very well with equation(S13). Therefore we determined the most probable value of t_(d) fromthese distributions with fits of equation (S14) to t_(d) histograms,which returned the location of the maximum in the histograms:

$\begin{matrix}{y = {y_{o} + {{Ae}^{({{- e^{\frac{({x - x_{c}})}{w}}} - \frac{({x - x_{c}})}{w} + 1})}.}}} & ({S14})\end{matrix}$

In this equation y_(o) is the baseline, A is the amplitude of the peak,x_(c) is the x-value at the center of the peak (i.e. the most probablevalue of t_(d)), and w is the width of the distributions. Based on theresults of this fit to the distributions of t_(d), we reported the valueof x_(c) and its error from the fit as the most probable t_(d) valuewith its associated error. To determine if the value of x_(c) wassensitive to the size of the bins in the t_(d) histograms, we generatedhistograms with different bin-widths from t_(d) values obtainedstreptavidin. In all cases the first bin began at 25 μs since this valuerepresents the lower limit for accurate detection and quantification oft_(d) (See Supplementary Section S9). FIG. 28 shows the resultinghistograms from bin widths of 15 μs, 30 μs, and 50 μs. In all threecases, the most probable t_(d) values (i.e. the value of x_(c))determined by the best curve fits of equation (S14) to t_(d) histogramswere within error of each other (with maximum deviations of 6 μs),demonstrating that this method of fitting distributions of t_(d) valuesfor determining the most probable t_(d) value was not sensitive to thebinning method in a range of bin widths from 15 to 50·s.

One of the advantages of using the most probable value of t_(d) forquantitative analysis compared to using, for instance, the average valueof t_(d), is that the absolute maximum in each distribution can bedetermined with high accuracy and small errors (smaller than 23% of themost probable value of t_(d)) from fits to histograms of t_(d). Thisapproach of determining the location of the absolute maximum is notsensitive to the possible presence of small sub-peaks in t_(d)histograms such as those present in some t_(d) distributions in FIG. 3in the main text.

Section S8. Calculating the Charge of Proteins from the TranslocationTime of Lipid-Anchored Proteins

S8.1 Derivation of Equation (3) in the Main Text

Based on recent work by Sexton et al, we developed the simplest possiblemodel that yields a relationship between t_(d), the lateral diffusioncoefficient of the lipids in the bilayer coating, D_(L), and the netcharge of a protein, |z|×e, where z (unitless) is the net valency of thecharge on the protein and e (C) is the elementary charge of anelectron³⁴.

This model assumed that the only driving force, f (N), acting on acharged, translocating protein is exerted by the electric field thatdrops inside the pore; it also assumed that inside of cylindricalnanopores the voltage V_(P) (V) drops linearly along the length of thepore, l_(p) (m):

$\begin{matrix}{f = {{z}e{\frac{V_{p}}{l_{p}}.}}} & ({S15})\end{matrix}$

Note that V_(p) refers only to the part of the total applied voltage,V_(a), that drops inside the pore, and it can be calculated byV_(p)=V_(a)×R_(p)/R_(total) (see Supplementary Equations (S3) and (S6)).Based on these assumptions, the charged protein experiences a constantforce opposed by a viscous drag inside the pore, leading to a constantnet electrophoretic drift velocity, ν (m s⁻¹):

$\begin{matrix}{{v = {\frac{l_{p}}{t_{d}} = \frac{f}{\zeta}}},} & ({S16})\end{matrix}$

where ζ (kg s⁻¹) represents the viscous friction coefficient. Assumingthat, for lipid-anchored proteins, ζ is dominated by the lipid anchor inthe bilayer²¹⁻²³, it can be expressed by the Stokes-Einsteinrelationship:

$\begin{matrix}{{\zeta = \frac{k_{B}T}{D_{L}}},} & ({S17})\end{matrix}$

where k_(B) (J K⁻¹) is the Boltzmann constant, T (K) is temperature, andD_(L) (m² s⁻¹) represents the lateral diffusion coefficient of lipids inthe bilayer. Combining equations (S15)-(S17) yields the desiredfunctional relationship between t_(d), the diffusion coefficients of thelipids in the bilayer coating, and the net charge of a translocatingprotein:

$\begin{matrix}{t_{d} = {\frac{l_{p}^{2}k_{B}T}{{z}e\; V_{p}D_{L}}.}} & ({S18})\end{matrix}$

This equation is the same as equation (3) in the main text.

In order to validate this model and the resulting equation (S18), weanalyzed translocation events of streptavidin molecules throughbilayer-coated pores with biotin-PE lipids while employing electrolytesolutions of various pH to vary the value of |z| according to Sivasankaret al³⁵. FIG. 5 of the main text shows that equation (S18) accuratelypredicted t_(d) as a function of z and could be used to determineparameters such as D_(L), l_(P), or |z|.

We further validated equation (S18), which is equation (3) in the maintext, by determining the most probable t_(d) values from translocationevents of the IgG antibody as a function of the voltage drop inside thenanopore, V_(p). FIG. 29 illustrates that t_(d) was indeed inverselyproportional to V_(p) as predicted by equation (S18). Moreover, fittingequation (S18) to the data in FIG. 29 revealed a net charge of theantibody of z=−4.2±0.5 with z as the only fitting parameter. This valuecompares well to the value of z=−3.6±2.3 determined by capillaryelectrophoresis (Section S8.2). We also used equation S18 to calculate anet average charge for the Fab fragment of −5.4±0.6 based on the mostfrequently observed t_(d) value in FIG. 3b of the main text. This valueis comparable to the charge that we determined by capillaryelectrophoresis (z=−4.3±0.4) or by fits to the distributions of t_(d)(z=−2.9±0.6) (see Sections S8.2 and 8.3). As a result, we reported arange for the values of z in the main text.

Note that in all experiments, we assumed that the pH value inside thenanopore was the same as the pH value in the bulk electrolyte solution.Since we carried out all protein translocation experiments in nanoporesthat were coated with electrically neutral phosphatidylcholine bilayersand since the KCl concentration of the electrolyte in these experimentswas 2.0 M, we did not expect significant differences between the pHvalue inside the pore and the value in the bulk solution.

S8.2 Capillary Electrophoresis for Determining the Net Charge ofProteins

To provide independent evidence that values of t_(d) can be used tocalculate the net charge of proteins used in this work, we determinedthe net charge of streptavidin (SA), anti-biotin antibody Fab fragments,and monoclonal anti-biotin IgG antibodies (mAb) from capillaryelectrophoresis (CE) experiments. FIG. 30a, b shows electropherogramsfor SA and Fab that we obtained using a CE instrument fromHewlett-Packard equipped with a UV absorbance detector. In eachelectropherogram, two peaks were present due to a transient increase inthe absorbance within the light-path of the detector near the end of thecapillary. The first peak was due to the so-called neutral marker (asmall molecule with a net charge of zero), 4-methoxybenzyl alcohol, andthe second peak was attributed to the protein. The difference betweenthe elution time for the neutral marker, t_(NM) (s), and the elutiontime, t_(A) (s), for a spherical protein is given by equation (S19)³⁶:

$\begin{matrix}{{z = \frac{L_{T}L_{D}6{\pi\eta}\; {R\left( {\frac{1}{t_{A}} - \frac{1}{t_{NM}}} \right)}}{V_{A}e}},} & ({S19})\end{matrix}$

where L_(T) (m) is the total length of the capillary, L_(D) (m) is thelength of the capillary to the detector, 11 (Pa×s) is the viscosity ofthe electrolyte (calculated in this work from equation (S8)), R (m) isthe effective radius of the protein, V_(A) (V) is the applied potentialdifference across the capillary, and e (C) is the elementary charge ofan electron. Based on the volume of the proteins, we estimated aneffective radius for SA of 2.9 nm (corresponding to 105 nm³) and for Fabof 3.2 nm (corresponding to 140 nm³). For the mAb, we used an effectiveradius of 5.5 nm that Jossang et al. determined from the diffusioncoefficient of IgG antibodies³². Table S3 lists the calculated charge ofSA and Fab that we determined from these CE experiments and comparesthese values to the ones determined from fits to the distributions oft_(d) values obtained during the nanopore translocation experiments.

Based on CE experiments, we measured slightly different values for thecharge of SA than those reported by Sivisankar et al; these deviationsincreased as the pH decreased. These discrepancies are likely due to thedifference in the charge of SA in solution compared the charge of SAbound to a surface by a biotin anchor. The reported pI of SA in solutionis 6.3³⁵ while Sivasankar et al. reported a pI of SA bound tobiotinylated lipids of 5-5.5 and Vlassiouk et al. reported a pI of SAbound to immobilized biotin on a surface of ˜5.5^(35,37). Since, theexperimental conditions used by Sivasankar et al. were very similar tothose used here (i.e. SA bound to biotinylated lipids in a lipid bilayercomposed of lipids with a head group of phosphatidylcholine), we plottedt_(d) values in FIG. 5 of the main text versus the values reported bySivasankar et al.

TABLE S3 Net valence, |z|, of the charge of proteins, diffusioncoefficients of proteins within the nanopore, D_(P), and diffusioncoefficients of lipids in the bilayer coating, D_(L). Lipid pH ofZ_(LITERATURE) D_(L) ^(d) D_(P) ^(c) Protein Bilayer^(a) electrolyte 35z_(CE) ^(b) z_(Td) ^(c) (nm² μs⁻¹) (nm² μs⁻¹) Δ_(D) % SA POPC 7.4 −1.9 ±0.4 −1.8 ± 0.1 −0.8 ± 0.2 1.13 ± 0.13 1.4 ± 0.1 +24 SA DΔPPC 7.4 −1.9 ±0.4 −1.8 ± 0.1 −1.1 ± 0.2 1.56 ± 0.16 1.7 ± 0.1 +9 SA POPC 8.0 −2.4 ±0.4 −2.8 ± 0.3 −2.3 ± 0.2^(f) 1.65 ± 0.17 1.8 ± 0.1^(f) +6 SA POPC 7.1−1.7 ± 0.4 −0.9 ± 0.2 −1.6 ± 0.1^(f) 1.65 ± 0.17 1.7 ± 0.1^(f) +6 SAPOPC 6.6 −1.2 ± 0.4 −0.7 ± 0.2 −1.0 ± 0.1^(f) 1.65 ± 0.17 1.4 ± 0.1^(f)−15 SA POPC 6.1 −0.8 ± 0.4 −0.3 ± 0.1 −0.9 ± 0.1^(f) 1.65 ± 0.17 1.0 ±0.1^(f) −39 SA POPC 5.7 −0.5 ± 0.4 — −0.9 ± 0.1^(f) 1.65 ± 0.17 1.2 ±0.1^(f) −21 Fab POPC 7.4 — −4.3 ± 0.4 −2.9 ± 0.6 1.27 ± 0.13 1.7 ± 0.1+31 mAb POPC 7.4 — Peak 1: −0.3 ± −4.2 ± 0.5^(e) 1.29 ± 0.13 1.8 ± 0.5+38 0.3 Peak 2: −3.6 ± 2.3 ^(a)All lipid bilayers also contained0.15-0.4 mol % of Biotin-PE. ^(b)Value of z_(CE) determined by capillaryelectrophoresis from equation (S19). ^(c)Value of z_(Td) and D_(P)determined by fitting the cumulative distributions of t_(d) withequation (S13), in which ν was described by equation (S20), with bothz_(Td) and D_(P) as fitting parameters. ^(d)Values for D_(L) determinedby FRAP as described in Supplementary Section S2. ^(e)Value of zdetermined from the fit in FIG. S17. ^(f)Values were determined byfitting equation S21 to histograms.

We performed a second set of CE experiments with a CE instrument fromBeckman equipped with fluorescence detection. To detect proteins withthis instrument, we incubated the anti-biotin IgG antibody withbiotin-5-fluorescein prior to performing the CE experiment. FIG. 30cshows the resulting electropherogram, which we used to calculate the netcharge of the mAb. Since biotin-5-fluorescein presumably has a netcharge of approximately −1 at pH 7.4, we subtracted 1 charge from thevalue of z determined with equation (S19) to calculate a net charge ofthe mAb. We observed two peaks in the presence of mAb, both of whichgrew in size with increasing concentrations of biotin-5-fluorescein.These two peaks did not overlap with the peak of unboundbiotin-5-fluorescein and could therefore both represent theantibody-ligand complex. These two peaks after the neutral marker inFIG. 30c correspond to z values of −0.3±0.3 and −3.6±2.3 (Table S3).

S8.3 Fitting Individual Distributions of t_(d) with Both z and D asFitting Parameters

To determine if parameters such as |z| and D_(L) could be extracted fromdistributions of t_(d) such as those shown in FIG. 3 in the main text,we incorporated the net valence of the charge, |z|, of a protein intoequation (S10) by combining it with equation (S20), which describes theelectrophoretic drift velocity, ν, based on equations (S15)-(S17):

$\begin{matrix}{v = {\frac{{z}e\; V_{P}D}{l_{P}k_{B}T}.}} & ({S20})\end{matrix}$

Substituting equation (S20) into equation (S10) resulted in equation(S21), which permitted the determination of the diffusion coefficient oflipid anchored proteins, D_(P), and the net valence of the charge of theproteins, |z|, in the nanopore based on best curve fits to individualdistributions of t_(d).

$\begin{matrix}{{P\left( t_{d} \right)} = {\frac{\left\lbrack {{\left( \frac{{z}e\; V_{P}D}{l_{P}k_{B}T} \right)t_{d}} + l_{P}} \right\rbrack \times e^{\frac{- {\lbrack{l_{P} - {{(\frac{{z}e\; V_{P}D}{l_{P}k_{B}T})}t_{d}}}\rbrack}^{2}}{4{Dt}_{d}}}}{t_{d} \times \sqrt{4{Dt}_{d}\pi}}.}} & ({S21})\end{matrix}$

Table S3 compares the values of |z| obtained with this method to theliterature values of |z| for SA, the values of |z| obtained with CE, thevalues of D_(P), and the values of D_(L) for SA, mAb, and Fab. For Fab,values of |z| and D_(P) determined with equation (S21) fromnanopore-based t_(d) distributions were in good agreement (±39%) withthe expected values as obtained from CE and from FRAP experiments.

For streptavidin, values of |z| determined by Sivasankar et al. agreedwell with the values determined by fitting t_(d) distributions fromtranslocation experiments with SA with equation (S21). The onlyexception was the experiment with streptavidin in an electrolyte with apH of 5.7. The difference in the value of |z| of Δz=0.4 in theelectrolyte with a pH of 5.7, is likely due to the reduced charge of SAat this pH (|z|=0.5±0.2)³⁵. This charge, which is close to neutral,presumably led to a shift from an electrophoretically dominated movementthrough the nanopore to a diffusion-dominated movement of SA.Consequently, a fraction of the recorded resistive pulses may have beendue to partial translocation events (i.e. diffusion of SA into and outof the same side of the nanopore). Such events could be associated withshorter than expected values for t_(d).

For the mAb, we observed two peaks in the CE data which corresponded totwo different charges for the mAb. One of the peaks corresponds to az=−3.6±2.3, which agrees well with the value of z=−4.2±0.5 determinedfrom the fit in FIG. 29. The second peak in the CE data corresponds to az=−0.3±0.3. If the charge of the mAb would indeed be −0.3±0.3, then someproteins may only partially move through the nanopore (as discussed forSA at pH 5.7), which may result in shorter than expected values fort_(d). Consequently, the predictions of the charge of the mAb based ont_(d) values would calculate values for z that are larger than the truevalue. However, based on the results in FIG. 29, the charge of the mAbis likely to be z=−3.6 rather than −0.3.

Section S9. Data Acquisition and Analysis of Resistive Pulses forProtein Detection

We used Ag/AgCl pellet electrodes (Warner Instruments) to monitor ioniccurrents through electrolyte-filled nanopores with a patch-clampamplifier (Axopatch 200B, Molecular Devices Inc.) in voltage clamp mode(i.e., at constant applied voltage). We set the analog low-pass filterof the amplifier to a cutoff frequency of 100 kHz. We used a digitizer(Digidata 1322) with a sampling frequency of 500 kHz in combination witha program written in Lab View to acquire and store data.

To detect resistive pulses caused by the translocation of proteinsthrough the nanopore, we applied a potential difference of ±0.1 V acrossthe nanopore. The polarity refers to the top fluid compartment thatcontained the protein while the other fluid compartment was alwaysconnected to ground. We recorded the resulting current with the maximumbandwidth of the recording setup (cut-off frequency, f_(c)˜50 kHz)³⁸ andwith a sampling frequency of 500 kHz using a custom program written inLabVIEW. To distinguish resistive pulses reliably from the electricalnoise, we used the software PClamp (Molecular Devices Inc.) to determinethe baseline of the current and to filter current recordings with adigital, Gaussian low-pass filter (f_(c)=15 kHz).

Using PClamp software, we performed a threshold-search for resistivepulses within the current recordings. We defined the start of aresistive pulse by a resistive decrease in the magnitude of the currentpast a threshold value that we set to 5× the standard deviation of thenoise of the baseline current. Based on this definition, typicalthreshold values ranged from 150 to 250 pA depending on the nanoporedimensions and the bilayer coating. The subsequent return of the currentpast a second threshold, which we set to one standard deviation of thenoise in the baseline current, and toward the baseline value, marked theend of the resistive pulse. We confirmed that for the analysis oftranslocation events from streptavidin and Fab, this procedure returnedthe same t_(d) values as a method based on half-widths of resistivepulse recently reported by Talaga and Li²⁴. Due to the large magnitudeand magnitude variability of resistive pulses in the antibodyexperiments, we determined t_(d) values based on the half-width ofresistive pulses from antibodies in a method similar to the approachdescribed by Talaga and Li²⁴. We defined ΔI as the maximum deviationfrom the baseline current within the time, t_(d).

To determine the time-response of the recording and analysis methodsexperimentally, we used a waveform generator (Agilent 33220A) to inputcurrent pulses in a method similar to Talaga and Li²⁴. These currentpulses had a ΔI of 650 pA with a rise time of 5 ns and durations rangingfrom 10 μs to 200 μs. Analyzing the data based on the half-width of thecurrent pulses, FIG. 31a shows that we could accurately measure themagnitude (ΔI) of resistive pulses if these pulses had t_(d) valueslarger than 50 μs and FIG. 31b shows that we could accurately determinet_(d) values that were larger than 25 μs. In all quantitative analysesof resistive pulses reported in this work, we constructed t_(d)histograms only from translocation events that lasted at least 25 μs andM histograms only from translocation events that lasted at least 50 μs(typically 70 μs).

To characterize the inherent measurement error of t_(d), σ_(t), of therecording and analysis methods, we added a current trace containingexperimentally recorded electrical noise from a resistive-pulseexperiment to current traces containing current pulses generated by awaveform generator. Thus, these current traces contained current pulseswith a precisely defined duration and contained a realisticrepresentation of the electrical noise in a resistive pulses experiment.Using the resulting current traces we determined t_(d) based on thehalf-width of the current pulses as described above. For current pulseswith a precisely defined duration, we measured a range of t_(d) valuesand FIG. 32 plots these values in histograms. We fit these histogramswith Gaussian distributions, and from the fit we determined that theinherent measurement error of t_(d) ranged from 2 to 4 μs and was notaffected by the magnitude of t_(d).

Section S10. Preparation of Amyloid-Beta Samples and Gel-Electrophoresis

We received Aβ peptides (residues 1-40, Aβ 1-40) in powder form from GLBiochem (Shanghai) Ltd with a purity above 98%. To remove aggregates ofAβ 1-40, we dissolved the powder in hexafluoroisopropanol (HFIP) to aconcentration of 1 mM of Aβ 1-40. After 24 h incubation in HFIP, wediluted this solution with cold (4° C.) deionized water at a 2:1 (v/v)ratio (H₂O:HFIP). We then rapidly aliquoted the solution, immediatelyfroze it in a CO₂/acetone bath, and lyophilized the frozen aliquots fortwo days to remove HFIP³⁹. To start the aggregation process of Aβ 1-40peptides, we dissolved the lyophilized powder in deionized water to aconcentration of 1 mg×mL⁻¹. We incubated these samples in siliconizedplastic microcentrifuge tubes on a temperature-controlled shaker at atemperature of 22° C. To detect aggregates of Aβ 1-40, we formed asupported lipid bilayer of POPC lipids on a chip containing a nanoporewith a diameter of 96 nm and a length of ˜275 nm (dimensions are beforethe lipid bilayer coating). We added solutions containing Aβ 1-40 to thetop solution compartment of the fluidic setup such that the finalconcentration of Aβ 1-40 ranged from 0.1 to 0.2 mg×mL⁻¹. We used arecording buffer containing 70 mM KCl and 10 mM HEPES with a pH of7.4±0.1 and recorded resistive pulses at an applied potential differenceof +0.2 V.

To confirm the presence of large aggregates of A□ peptides in thesesamples independently, we performed a Western blot with solutionscontaining Aβ(1-40) that were allowed to aggregate for 0, 24, 48, and 72h. Prior to performing the electrophoresis, we followed a standardprotoco1⁴⁰ and cross-linked Aβ(1-40) samples (1 mg mL⁻¹) with 0.04%glutaraldehyde for 20 min at room temperature and stopped the reactionby adding 200 mM of Tris. We diluted the cross-linked samples to 0.01 μgμL⁻¹ in native sample buffer (Bio-Rad), containing 10% (v/v) sodiumdodecyl sulfate. To resolve aggregates of Aβ(1-40) of differentmolecular weights we used a polyacrylamide gel: 18% Tris-HCl Ready Gel(Bio-Rad) in Tris-Glycine buffer. After running the gel, we transferredproteins to a polyvinylidene fluoride (PVDF) membrane (PerkinElmer LifeScience) and blocked the membrane for 1 h with TBS buffer containing 5%(w/v) nonfat dry milk and 0.0625% (w/v) Tween20. We incubated themembrane with a primary antibody against Aβ(1-40) (6E10 from Covance)for 1.5 h. An IgG anti-goat antibody served as the secondary antibodyand was incubated with the membrane for 1 h. We developed the membraneonto film using enhanced chemiluminescence (ECL, PerkinElmer LifeSciences). FIG. 33 shows the resulting Western blot and the increasingmolecular weights of Aβ(1-40) aggregates with increasing incubationtime. Note the presence of fibrillar aggregates with molecular weightsgreater than 250 kDa that remained in the wells of the polyacrylamidegel. Also note that the amount of these fibrillar Aβ(1-40) aggregates inthe wells of the gel increased with increasing time of aggregation.

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Supporting Information Single Particle Characterization of AD Oligomersin Solution.

S11. Nanopores without a Fluid Lipid Coating Clog Due to Adsorption ofAβ

See FIGS. 34 and 35.

S12. Preparation of Aβ Aggregates and Nanopore-Based Sensing Experiments

We received Aβ₍₁₋₄₀₎ peptides in powder form from GL Biochem (Shanghai)Ltd with a purity above 98%. To remove aggregates of Aβ₍₁₋₄₀₎, wedissolved the powder in hexafluoroisopropanol (HFIP) to a concentrationof 1 mM of Aβ₍₁₋₄₀₎.² After 24 h incubation in HFIP, we diluted thissolution with cold (4° C.) deionized water at a 2:1 (v/v) ratio(H₂O:HFIP). We then rapidly aliquoted the solution, immediately froze itin a liquid nitrogen bath, and lyophilized the frozen aliquots for twodays to remove HFIP. To start the aggregation process of Aβ₍₁₋₄₀₎peptides, we dissolved the lyophilized powder in deionized water to aconcentration of 1 mg×mL⁻¹. We incubated these samples in 0.5 mL closedsiliconized plastic microcentrifuge tubes on a temperature-controlledshaker (Thermocycler, Eppendorf) set to 750 rpm at a temperature of 22°C. for zero, one, two and three days.

To detect aggregates of Aβ₍₁₋₄₀₎, we first formed a supported lipidbilayer of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC)lipids (Avanti Polar Lipids, Inc.) on a nanopore that was 28 nm indiameter and had a length of 18 nm, resulting in a coated diameter ofapproximately 18 nm and coated length of 28 nm.¹. We described detailsof the bilayer formation in Yusko et al.¹ We added solutions containingAβ₍₁₋₄₀₎ to the top solution compartment of the fluidic setup (2 M KClwith 10 mM HEPES pH 7.4) such that the final concentration of Aβ₍₁₋₄₀₎ranged from 0.07 to 0.025 mg×mL⁻¹. We recorded resistive pulses at anapplied potential difference of −0.2 V with the polarity referring tothe top fluid compartment relative to the bottom fluid compartment,which was connected to ground. Recordings were completed within 10 to 15minutes of adding Aβ₍₁₋₄₀₎.

We used Ag/AgCl pellet electrodes (Warner Instruments) to monitor ioniccurrents through electrolyte-filled nanopores with a patch-clampamplifier (Axopatch 200B, Molecular Devices Inc.) in voltage-clamp mode(i.e., at constant applied voltage). We set the analog low-pass filterof the amplifier to a cutoff frequency of 100 kHz. We used a digitizer(Digidata 1322) with a sampling frequency of 500 kHz in combination witha program written in LabView to acquire and store data.³ To distinguishresistive pulses reliably from the electrical noise, we first filteredthe data digitally with a Gaussian low-pass filter (f_(c)=15 kHz) inMATLAB and then used a modified form of the custom written MATLABroutine described in Pedone et al.⁴ We modified the MATLAB routine tocalculate the translocation time, t_(d), as the width of individualresistive-pulse at half of their peak amplitude, also known as thefull-width-half-maximum value.^(1,5) From this analysis we obtained theΔI and t_(d) values for each resistive pulse.

S13. Gel Electrophoresis Experiments

To confirm the presence of aggregates of Aβ peptides in the samples, weperformed a Western blot with solutions containing Aβ₍₁₋₄₀₎ that wereallowed to aggregate under the same conditions for zero to three days.¹Prior to performing the electrophoresis, we aliquoted 0.5 μL of 1mg×mL⁻¹ Aβ₍₁₋₄₀₎ (in pure water) into 38 μL of pure water or into 38 μlof 2 M KCl, resulting in a concentration of Aβ₍₁₋₄₀₎ of 0.0129 mgmL⁻¹—roughly the same concentration used in the nanopore-basedcharacterization. We immediately cross-linked these Aβ₍₁₋₄₀₎ samples byadding 4 μL of 0.6875% (v/v) glutaraldehyde in water. After 10-20 min atroom temperature, we stopped the cross-linking reaction by adding 44.7μL of 200 mM Tris buffer. We aliquoted 10 μL of these samples into 20 μLof Native Sample Buffer (Bio-Rad: 62.5 mM Tris-HCl pH 6.8, 40% glycerol,0.01% Bromophenol Blue), which we modified to also contain 10% (v/v)sodium dodecyl sulfate (SDS) and 0.02 M β-mercaptoethanol. To resolveaggregates of Aβ₍₁₋₄₀₎ of different molecular weights, we used apolyacrylamide gel: 16.5% Tris-Tricine Ready Gel (Bio-Rad) inTris-Tricine buffer or a 7.5% Tris-HCl Ready Gel (Bio-Rad) inTris-Glycine Buffer following standard electrophoresis protocols.⁶ Afterrunning the gels, we transferred proteins to a polyvinylidene fluoride(PVDF) membrane (PerkinElmer Life Science) and blocked the membrane for1 h with TBS buffer containing 5% (w/v) nonfat dry milk and 0.0625%(w/v) Tween-20. We incubated the membrane with a primary antibodyagainst Aβ₍₁₋₄₀₎ (6E10 from Covance) for 1.5 h. An IgG anti-goatantibody conjugated to horseradish peroxidase served as the secondaryantibody and was incubated with the membrane for 1 h. We developed themembrane onto film using enhanced chemiluminescence (ECL, PerkinElmerLife Sciences). FIG. 36 shows the results of these gel electrophoresisexperiments.

FIG. 36 confirms that the procedure described above generates aqueoussolutions containing mostly pentameric Aβ₍₁₋₄₀₎ aggregates or smalleraggregates on day zero and increasingly larger aggregates after one,two, or three days of aggregation time. FIG. 36 also shows theaccelerated aggregation of Aβ₍₁₋₄₀₎ in the presence of 2 M KCl for ˜20min (the shortest possible time for the gel electrophoresis procedure).Regardless of this accelerated aggregation, time-dependent aggregationto higher molecular weight aggregates is apparent by the increasinglydarker bands in the wells, where fibers are retained, over time.Additionally, FIG. 36B highlights that in the 50-250 kDa aggregatesincreasingly larger aggregates develop between 1 and 3 days ofaggregation, eventually resulting in a relatively darker, larger band inthe well on Day 3 compared to Days 1 and 2. This result is importantsince 50 kDa is approximately the minimum molecular weight ofprotofibrils and marks the beginning of the transition from sphericaloligomers into cylindrical protofibrils.⁷ We confirmed by TEM analysisthat the increased aggregation rate due to the high ionic strength didnot affect the morphology of the fibrils (see Supporting InformationS18).

S14. Additional Comparison of Aβ Aggregates Sizes Determined byNanopore-Based Characterization and TEM.

To cross-examine our assumptions and results from the cluster analysis,we applied equation (2) to ΔI values from cluster (i) to estimate across-sectional area of aggregates in this cluster, and we appliedequation (1) to ΔI values from clusters (iii) and (iv) to estimate theexcluded volumes of these aggregates; this analysis ignores therequirement for l_(M)<L_(eff) for equation (1) and l_(M)>L_(eff) forequation (2). Finally, we searched the TEM images (FIG. 3 in the maintext and Supporting Information S8) for aggregates with the sizespredicted by this analysis and did not find aggregates in the TEM imageswith these sizes or shapes. For instance, if we incorrectly applyequation (2) to the data in cluster (i) (i.e. if we enforce thataggregates in cluster (i) have l_(M)>l_(eff)), we obtain cylindricaldiameters of 1.9 nm. We did not observe elongated aggregates of Aβ₍₁₋₄₀₎with diameters this small in the TEM images, suggesting that aggregatesclassified in cluster (i) should indeed be approximated as sphericaloligomers with equation (1) in the main text in agreement with theapproach that we used. Similarly, if we incorrectly assume that therequirement of l_(M)<l_(P) for equation (1) was satisfied by themolecules represented in clusters (iii) and (iv), we obtained sphericaldiameters of 9.4 nm and 12.6 nm, respectively. We typically did notobserve spherical aggregates of Aβ₍₁₋₄₀₎ with diameters greater than 9nm in the TEM images (i.e. only 10 out of 347 observed aggregates hadspherical diameters of 9 nm or larger), suggesting that the aggregatesrepresented in cluster (iii) are indeed protofibrils and that theaggregates represented in cluster (iv) are indeed fibers longer than theeffective length of the nanopore, again in agreement with the approachwe used in the main text.

These results show that the cluster assignment of translocation eventsby statistical cluster analysis of M and t_(d) values of each eventyielded diameter and lengths of Aβ aggregates that are consistent withobservations by TEM.

S15. Distributions of to Values in Clusters (i) and (ii)

Discussion about the Results in FIG. 37:

The observation that almost all translocation events in cluster (ii) hada t_(d) value between 35 μs and 45 μs compared to the more distributedt_(d) values in cluster (i) suggests that the aggregates in cluster (ii)had increased electrophoretic mobility.^(5,8) The resulting shorter timefor translocation through the pore minimized time-dependent diffusionalspreading and, therefore, led to a narrower distribution of t_(d) valuescompared to events in cluster (i). The reasons for this increasedelectrophoretic mobility of events in cluster (ii) could be decreasedinteractions with the lipid bilayer coating¹ or an orientation of theaggregate in the nanopore that reduces viscous drag, such as a prolateor cylinder moving with its long axis parallel to the direction ofmovement.⁹ As a third possibility, this result could be due to anincreasing charge per aggregate at a constant charge per monomeraddition, if electrostatic effects are neglected and we assume sphericalaggregates. With the latter two assumptions, the mathematicalrelationship between the most-probable translocation time, diffusionconstant, charge, and molecular weight involves equations (S1)-(S3):

$\begin{matrix}{{{z} = {{\frac{- 3}{4.3{kDa}}} \times N}},} & ({S1}) \\{{D = \frac{k_{B}T}{6{{\pi\eta}\left( \frac{3{M.W.}}{4{\pi A}_{v}\rho} \right)}^{1/3}}},} & ({S2})^{9} \\{and} & \; \\{t_{d} = \frac{l_{P}^{2}k_{B}T}{{z}e\; V_{P}D}} & ({S3})^{1}\end{matrix}$

where, z is the net charge valence of the aggregate, N is the number ofmonomers in the aggregate, D (m² s⁻¹) is the diffusion constant of theaggregate, M. W. (kDa) is the molecular weight of the aggregate (i.e.here 4.3 kDa×N), k_(B) (J K⁻¹) is Boltzmann's constant, T (K) is thetemperature, η (Pa s) is the viscosity of the solution, A_(ν) isAvagadro's number, ρ (kDa m⁻³) is the molecular weight density of aminoacids in a protein, l_(P) (nm) is the length of the nanopore, e (C) isthe elementary charge of an electron, and V_(P) (V) is the voltage dropacross the nanopore. The factor of −3/4.3 kDa in equation (1) isincluded to account for the expected net charge per Aβ₍₁₋₄₀₎ monomer of−3 and the molecular weight of a monomer of 4.3 kDa.^(10,11) Bycombining equations (S1)-(S3), we solved for t_(d) as a function of thenumber of monomers in the aggregate, V_(P), and a constant c to yieldequation (S4):

$\begin{matrix}{t_{d} = \frac{c}{N^{2/3}V_{P}}} & ({S4})\end{matrix}$

FIG. 38 shows a plot of equation (S4) and illustrates the trend inmost-probable translocation times for aggregates with increasingmolecular weight, assuming a constant charge to mass ratio, a constantapplied voltage, a spherical aggregate, and an aggregate with a lengthless than the length of the nanopore. This analysis shows thatincreasing the number of monomers in a low-molecular weight aggregatecould conceivably increase the electrophoretic force more than theviscous drag force, resulting in decreased translocation times that aremore narrowly distributed^(5,8) as the aggregates molecular weight, andhence charge, increases. This analysis does not apply to aggregates inclusters (iii) or (iv), since those aggregates have lengths longer thanthe length of the nanopore.

S16. Protofibril Diameters as a Function of their Length Determined byTEM Analysis.

See FIG. 39.

S17. Estimation of Protofibril Lengths

To generate histograms of the lengths of aggregates in clusters (i) and(ii) of the main text (FIG. 3), we expected that these aggregates wereprotofibrils elongating with a constant diameter¹² and hence had anarea-equivalent cylindrical diameter, 8c, of 4.4 nm (Table 1 in the maintext). We also expected that protofibrils were oriented with theirlength, l_(M), parallel to the length of the nanopore and hence electricfield.¹³⁻¹⁵ We defined the excluded volume of an aggregate and the shapefactor of an aggregate as a function of its length and solved a systemof equations for γ and l_(M) based on the ΔI value of each translocationevent.

Since TEM analysis (Supporting Information S16) and data in theliterature¹² show that the diameter of protofibrils is relativelyconstant and independent of length, we defined their excluded volume asthe volume of a perfect cylinder:

Λ=¼πθ_(c) l _(M),  (S5).

Substituting equation S5 into equation (1) of the main text yields ΔI asa function of γ and l_(M):

$\begin{matrix}{{\Delta \; {I\left( {\gamma,I_{M}} \right)}} = {{\frac{\gamma \; V_{A}{\pi\theta}_{c}I_{M}}{4{\rho \left( {I_{P} + {1.6r_{P}}} \right)}^{2}}\mspace{14mu} {for}\mspace{14mu} I_{M}} < {I_{eff}.}}} & ({S6})\end{matrix}$

To estimate a shape factor for this analysis, we used equations derivedby Fricke^(16,17) that describe the shape factor of spheroidal prolateparticles. A prolate can be described by three dimensions of lengths, a,b, and c. For a perfectly ellipsoidal (spheroidal) prolate, b=c, and inCartesian coordinates it is described by x²/c²+y²/b²+z²/a²=1. Equationsyielding the same shape factor, but through a different derivationprocesses that can be extended to non-symmetirc spheroids, can be foundin reports by Golibersuch, Deblois et al., and Osborn.¹⁸⁻²¹ According toFricke, when the longest axis, a, is parallel to the electric field, theshape factor, γ_(∥), is:

$\begin{matrix}{{\gamma_{||} = \left\lbrack {\frac{m^{2}}{m^{2} - 1} - \frac{m\; {\cosh^{- 1}(m)}}{\left( {m^{2} - 1} \right)^{3/2}}} \right\rbrack^{- 1}},} & ({S7})\end{matrix}$

where m=a/b=a/c and is greater than 1. Since we define the diameter ofthe aggregates in this section as θc=4.4 nm, we set m=1M/θc and rewriteequation S7:

$\begin{matrix}{\gamma_{||} = {\left\lbrack {\frac{\left( {I_{M}/\theta_{c}} \right)^{2}}{\left( {I_{M}/\theta_{c}} \right)^{2} - 1} - \frac{\left( {I_{M}/\theta_{c}} \right){\cosh^{- 1}\left( {I_{M}/\theta_{c}} \right)}}{\left( {\left( {I_{M}/\theta_{c}} \right)^{2} - 1} \right)^{3/2}}} \right\rbrack^{- 1}.}} & {({S8}).}\end{matrix}$

Finally, we solved equations S6 and S8 using MATLAB to obtain values ofγ and 1M for each aggregate based on its ΔI value. The lengths obtainedfor the aggregates are shown in a histogram in FIG. 3 of the main text.The values for γ in cluster (i) ranged from 1.5 to 1.2 with an averageof 1.35, and in cluster (ii) γ ranged from 1.048 to 1.2 with an averageof 1.13.

While the analysis above provides a good first approximation for thelengths of aggregates in clusters (i) and (ii), we would like to pointout two important limitations of this method. First, since theaggregates in cluster (i) are significantly shorter than the length ofthe nanopore, it is possible that the shortest ones among them rotatewithin the nanopore and thus do not have a constant shape factor. We canestimate an average shape factor if we consider the shape factor of aprolate with its axis a perpendicular to the electric field:

$\begin{matrix}{{\gamma_{\bot} = \frac{2\gamma_{||}}{{2\gamma_{||}} - 1}},} & {({S9}).}\end{matrix}$

The average shape factor for a prolate free to rotate about all axesis²⁰:

γ_(AVG)=⅓γ_(∥)+⅔γ_(⊥).   (S10).

Using the average shape factor relationship in equation (S10) for theaggregates in cluster (i) and MATLAB to solve equations (S6) and(S8)-(S10) yields the lengths shown in Figure S8A and a shape factorthat ranged from 1.50-1.52. This value is nearly identical to the shapefactor of 1.5 commonly used for spherical objects (i.e. the shape factorwe used to calculate the excluded volume for cluster (i) in Table 1 ofthe main text). We should highlight, however, that even a spheroidalprolate that is slightly elongated, will not be free to rotatehorizontally (i.e. with axis a perpendicular to the electric field)through the entire nanopore due to steric hindrances. FIG. 40Bapproximates the fraction of pore area (cross-sectional area) that acylinder of length l_(M) could occupy while in a horizontal orientation.Thus, it is likely that aggregates in cluster (i) and cluster (ii) willbe aligned in the nanopore due to the converging electric field as wellas steric effects. In reality the smallest aggregates in cluster (i) mayrotate while the longest aggregates are aligned in the electric field.This effect would close the mathematically created gap between thedistributions of lengths for the aggregates in clusters (i) and (ii)(Figure S8A).

The second concern with the analysis at the beginning of this sectionsstems from defining the geometry of aggregates in clusters (i) and (ii)as cylindrical (since TEM images revealed that the diameter of manyaggregates remained constant independent of length, Supporting SectionS16) while applying the shape factor for a prolate. An alternativeapproach is to define the shapes of the aggregates as spheroidalprolates rather than cylinders. The excluded volume of a perfectspheroidal prolate is:

Λ=4/3πbca

or using the parameter symbols in this work

Λ=⅙πθ_(c) ² l _(M)  (S11).

Solving the system of equations described above with equation (S11)replacing (S5) yields the distribution of lengths shown in FIG. 41. Asbefore, we assumed that all aggregates were aligned with their lengthaxis parallel to the length of the nanopore and the electric field. Theshape factor for the aggregates in cluster (i) ranged from 1.10-1.25with an average value of 1.17, and for the aggregates in cluster (ii) γranged from 1.02 to 1.10 with an average value of 1.07. If we assumethat the aggregates in cluster (i) can rotate in three dimensions, as inthe previous paragraph, then the average shape factor for the aggregatesin cluster (i) is 1.55, and the distribution of lengths is slightlynarrower than those shown in FIG. 41. Note that the lengths in thisdistribution are ˜1.5 times the lengths shown in FIG. 3 of the maintext. This result is a consequence of the fact that for a prolate andcylinder with the same volume, the prolate will have a length 1.5 timesthat of the length of the cylinder. Again, the best method probably liesbetween estimating the volumes of aggregates based on the shape of acylinder and the shape of a prolate.

To summarize this section, we estimated the lengths of aggregates inclusters (i) and (ii) by solving a system of equations includingγ(l_(M)) and 4/(γ, l_(M)). The resulting lengths and shape factors weredependent on whether the volume of the aggregate was constrained to acylindrical shape or a prolate spheroid shape. Regardless, the resultingdistributions of lengths suggest that local maxima occur in thedistributions of protofibril lengths as predicted by Cabriolu et al.²²

S18. Preparation of Transmission Electron Microcopy Samples

We prepared samples for transmission electron microscopy (TEM) analysisusing a negative staining method and glow-discharged, carbon-coatedcopper grids (Electron Microscopy Sciences, Cat no: FCF-200-Cu). Weapplied 5 μL of each Aβ sample (1 mg×mL⁻¹), which had been permitted toaggregate in pure water for zero, one, two, or three days, to theglow-discharged carbon coated copper grid. After 2 min, we wicked offthe fluid on the grids with filter paper and washed the grids with a 5μL drop of deionized water for 1 min. After wicking off the fluid again,we applied a 5-4, drop of 2% uranyl acetate for 1 min, wicked off theexcess fluid on the grids, and allowed the grids to dry.

To examine the morphology of aggregates formed in 2 M KCl, we performeda slightly different procedure. We diluted the 1 mg×mL⁻¹ sample ofAβ₍₁₋₄₀₎ to a concentration of 0.05 mg/mL in 2 M KCl. We immediatelymixed this solution using a vortex shaker and applied 5 μL of the sampleto the glow-discharged carbon coated grids. After 10 min, we wicked offthe fluid on the grids with filter paper and washed the grids threetimes with 5 μL deionized water (1 min each time). After wicking off thefluid again, we applied a 5-μL drop of 2% uranyl acetate for 1 min,wicked off the excess fluid on the grids, and allowed the grids to dry.We examined the images of negatively stained Aβ structures using a JEOL3011 high resolution electron microscope (Jeol Ltd., Tokyo, Japan).

FIG. 42A shows several TEM images of Aβ₍₁₋₄₀₎ aggregates that were firstprepared in pure water like all samples in this work and then exposed to2 M KCl for 10 min. We analyzed the dimensions of the aggregates in thesame manner as FIG. 3 in the main text. For all parameters, themorphology of aggregates that were exposed to 2 M KCl for 10 min, as inthe resistive-pulse sensing experiment, was the same as the morphologyof aggregates prepared only in pure water (FIG. 3 main text). Table S1.summarizes the characterized parameters. For instance, the diameter ofprotofibrils and fibers were nearly identical between the twopreparations. The range of lengths of the protofibrils were similarbetween the two treatment methods; however, the probability of observinglong protofibrils was slightly higher in samples exposed to 2 M KCl(i.e. P(l_(M)>45 nm) on Day 1-2 of ˜0.3-0.4) compared to the samplesthat were not exposed to KCl (i.e. P(l_(M)>45 nm) on Day 1-2 of˜0.15-0.2) (FIG. 3C inset in the main text and Figure S9C inset). Thissuggests that brief incubation in solutions with high ionic strengthsaccelerates the time-dependent aggregation of Aβ such that the number ofAβ aggregates increases, which enables the formation of protofibrilswith longer lengths than those produced in solutions in low ionicstrengths.

TABLE S1 Morphology of Aβ₍₁₋₄₀₎ aggregates exposed only to pure waterand aggregates that were exposed to 2M KCl for 10 min. Errors arestandard deviations from the mean value. Distance Spher- Proto- FiberFiber between ical θ fibril θ x-over θ flat θ x-overs Treatment nm nm nmnm² nm Pure Water 6.2 ± 1.2 6.3 ± 1.5 5.6 ± 0.8 11.5 ± 1.5 97 ± 27 N =18 N = 117 N = 27 N = 27 N = 27 10 min 7.2 ± 1.5 6.5 ± 1.1 5.4 ± 1.012.7 ± 2.3 80 ± 9 exposure N = 32 N = 178 N = 7 N = 7 N = 6 to 2M KCl

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What is claimed is:
 1. A method of detecting, quantifying, orcharacterizing a biomolecule, collection of biomolecules, or particles,comprising: providing a transit path for biomolecules or particles topass through a nanopore from a first liquid compartment to a secondliquid compartment, wherein the first and second liquid compartmentscontain electrodes disposed to measure voltage difference, current flow,or resistance between the first and second liquid compartments; andmeasuring voltage difference, current flow, or resistance between thetwo liquid compartments over time as individual biomolecules passthrough the nanopore; wherein the nanopore is a passageway through asubstrate, which passageway is lined with a fluid wall, wherein thefluid wall comprises an amphipathic molecule, a bilayer, a surfactant,or a detergent, or wherein the fluid wall further comprises a lipidanchored ligand.
 2. The method according to claim 1, wherein the fluidwall comprises an amphipathic molecule.
 3. The method according to claim1, wherein the fluid wall comprises a bilayer.
 4. The method accordingto claim 1, wherein the fluid wall comprises a surfactant or adetergent.
 5. The method according to claim 1, wherein the nanopore ischaracterized by a nominal width perpendicular to the transit path thatis about 1.5 to about 50 times the dimension of the biomolecule orparticle and wherein the length of the nanopore parallel to the transitpath is one to five times its nominal width.
 6. The method according toclaim 1, wherein the fluid wall comprises a monolayer.
 7. The methodaccording to claim 1, wherein the fluid wall further comprises a lipidanchored ligand.
 8. The method according to claim 7, wherein the lipidanchored ligand comprises an antibody.
 9. The method according to claim1, wherein the nanopore has a nominal width of 10 to 200 nanometers. 10.The method according to claim 1, wherein the nanopore has a nominalwidth of 20 to 30 nanometers.
 11. The method according to claim 1,wherein the biomolecule comprises a protein or protein aggregate. 12.The method according to claim 1, wherein the biomolecule comprises anucleic acid.
 13. The method according to claim 1, wherein thebiomolecule comprises an antibody.
 14. The method according to claim 11,wherein the protein is an amyloid β protein.